# A novel algorithm for clearing financial obligations between companies - an
application within the Romanian Ministry of Economy

Lucian-Ionut Gavrila  Faculty of Mathematics and Computer Science University
of Bucharest, Romania  Alexandru Popa  National Institute for Research and
Development in Informatics

###### Abstract

The concept of clearing or netting, as defined in the glossaries of European
Central Bank, has a great impact on the economy of a country influencing the
exchanges and the interactions between companies. On short, netting refers to
an alternative to the usual way in which the companies make the payments to
each other: it is an agreement in which each party sets off amounts it owes
against amounts owed to it. Based on the amounts two or more parties owe
between them, the payment is substituted by a direct settlement. In this paper
we introduce a set of graph algorithms which provide optimal netting solutions
for the scale of a country economy. The set of algorithms computes results in
an efficient time and is tested on invoice data provided by the Romanian
Ministry of Economy. Our results show that classical graph algorithms are
still capable of solving very important modern problems.

##  1 Introduction

According to the European Central Bank Glossary of terms related to payment,
clearing and settlement systems [2] the concept of netting (also known as
clearing) between entities is defined as “an arrangement among three or more
parties for the netting of obligations and the settling of multilateral net
settlement positions”. Companies acting in an economy express their
interaction by issuing invoices one to another. These invoices imply an
obligation of payment, which is normally settled through a bank transfer.
Netting offers an alternative to direct payments. For example, considering two
companies, a national transportation provider and a national energy provider,
they interact and issue invoices to each other. Therefore, they have mutual
debts which can be settled through netting, instead of a direct payment.

In this paper, we consider a particular netting approach that involves
computing circuits of debts between companies and settling them. For example,
company A has to pay an amount of 32.000 USD to company B, which has to pay
23.000 USD to company C, which has to pay 25.000 USD to company A. Through a
clearing system, a netting circuit is determined between companies A, B and C.
The option of clearing the minimum amount of 23.000 USD is presented to them.
If the companies accept the clearing, the minimum amount will be subtracted
from the payment obligations. Therefore, company A remains to pay 9.000 USD to
B, B has no more payment obligations to C, C remains to pay 2.000 USD to A.
The remaining amounts can be considered in other netting circuits. Netting
brings important advantages like reducing the delays implied by bank
transfers, reducing the number of transfer transactions, providing lower costs
by avoiding the transfer fees, improving the credit risk [7]. According to
[3], “by reducing the number and overall value of payments between financial
institutions, netting can enhance the efficiency of payment systems”. In
financial crisis scenarios, small, medium and in some cases even large scale
companies do not have the necessary liquidity to face their financial
obligations. This idea is outlined in [4] in a similar manner for the banking
system. Chen and Wu [4] present the fact that netting brings changes to the
network dependence and connectivity, lowering the impact of financial shocks
by reducing debts between banks.

Therefore, an efficient netting system generates an important help in reducing
the risk of insolvency for companies and, in a broader picture, in reducing
the systemic risk and saving the economy from a domino effect [7].

#### Connection with graph theory.

A netting system can be rendered in terms of graph theory. Every company can
be represented as a node in a graph. A directed edge between two nodes
designates the fact that one of the companies issued a set of invoices to the
other. Given two nodes $u$ and $v$ we may have simultaneously the edges
$(u,v)$ and $(v,u)$ , considering that each company has issued invoices to the
other. In this situation, the meaning is that a company is not only a customer
but also a provider to the counterparty company.

#### Motivation.

The goal of this paper is to present algorithms that improve the netting
system in Romania. Our tests use the _real data_ provided by the system for
debt and credit clearing which runs under the supervision of the Institute of
Management and Informatics, the Romanian Ministry of Economy.

According to the public data, between 1999 and 2017, a total amount of more
than 240 billion RON was netted (more than 60 billion Euros). This amount
represents an important percentage of the annual GDP of Romania. One has to
reflect on the idea that the cleared amount was based on circuits determined
in an empirical manner. The circuits were identified manually, by the fact
that the companies knew their partners and proposed clearing solutions.
Therefore, the netting solutions were not provided with the aid of an
automated system of algorithms. The implementation of an efficient flow of
algorithms which run at the level of an economy for an entire country provides
great benefits to the economic environment. A table of the public results
issued by the Institute of Management and Informatics from Romania is
presented in Figure 1, with more details in [11].

Starting from the 1st of January 2020, the netting platform in the Institute
of Management and Informatics (IMI), Romanian Ministry of Economy, was
upgraded to use the algorithms proposed in this paper in order to automate the
process of circuits computation. In January 2020, more than 100 million Euros
were netted by using our computation model.

Figure 1: Netting amounts - Romanian Institute of Management and Informatics,
2000 - 2017

#### Previous and related work.

The concept of netting has been described in numerous papers related to
financial markets, commerce and economy. Some of the most important results
were published in [17, 14, 10, 19, 13]. Netting is mainly involved and
generates the best results in interbank payments and in cash optimization for
corporation branches in an international environment [10]. Güntzer, Jungnickel
and Leclerc [10] outline the idea that interbank payments represent a process
which involves high volumes of participants and large amounts of money, with
an example focused on the Germany’s interbank payment system. Srinivasan and
Kim [17] highlight the importance of payment netting between multinational
corporations and claim that corporations generate larger and larger volumes of
inter-company money flows. Therefore, by implementing an efficient clearing
system one can obtain significant savings in payment and interest costs. Csoka
and Hearings [6] present the importance of clearing in relation with financial
systemic risk and suggest a decentralized clearing method based on a clearing
payment matrix. In the literature of financial networks, a set of algorithms
for the determination of the greatest clearing payment matrix have been
outlined by Eisenberg and Noe [8], Elliot [9], Rogers and Veraart [15].

The aforementioned papers motivate the significance of netting in systems like
interbank payments or large corporations. As we show in this paper, the
concept of netting can be extended to a larger scale. The only application of
a clearing system at the scale of a country economy is known to function in
Romania. In the Romanian system, the acting parties are represented by every
economic agent, regardless of its size.

For solving clearing problems multiple approaches have been proposed. For
example, [10] presents some simple and efficient heuristic algorithms to
accommodate the netting problem. According to [16], Shapiro formulated the
multinational payment clearing problem in terms of linear programming, while
Srinivasan and Kim present in [17] a network optimization approach considered
not only as computationally efficient but also intuitively appealing. For the
netting problem based on inter-company invoices, Kumlander [13] outlines a set
of practical clearance algorithms in based on graph theory. According to [1],
clearing problems that have bounds on the length of the circuits are NP-hard.
Thus, according to the conjecture that $P\neq NP$, polynomial time exact
algorithms for this problem are unlikely to exist.

#### Our results.

In this paper, we propose an alternative approach for computing efficient
netting solutions. Considering the peculiarities of invoice netting and the
fact that the netting circuits length can have an upper limit, we propose a
set of graph theory algorithms to find the exact circuits in an invoice graph.
It is worth mentioning that our algorithms are already accepted as an upgrade
for the Debt and Credit Clearing system running under the Romanian Ministry of
Economy authority, the Institute of Management and Informatics. The algorithms
are integrated into the netting platform since the 1st of January 2020. In
three weeks, the processed sums exceed 100 million Euros. Our paper is the
only one proposing a system for debt and credit clearing at the scale of a
country economy.

The context of invoice netting has a much larger set of input and output data
in comparison with interbank and corporate netting. Thus, an integer
programming approach cannot efficiently process such a large amount of data.
In our algorithms, the most important part is the circuit identification,
based on Johnson’s algorithm [12]. According to Leiserson’s analysis in [5],
Johnson’s algorithm is a polynomial time algorithm. It is based on two widely
known subroutines, Bellman-Ford (in order to eliminate negative edges) and
Dijkstra’s shortest path algorithm. The efficiency of our solution, in
comparison with heuristic approaches, comes from the fact that the invoice
graph is splitted into strongly connected components which reflect the
interaction of companies in the economy. By splitting the main problem into
smaller similar problems, we obtain an efficient running time. For every
connected component, we compute a set of netting circuits. Another advantage
of our solution is that, for every set of the netting circuits from a strongly
connected component, we compute the best settlement order in terms of maximum
clearing amount.

Our algorithm has the following main steps:

  1. 1.

represent a directed graph based on invoice information;

  2. 2.

compute the strongly connected components of the graph using Tarjan’s
Algorithm;

  3. 3.

determine the elementary circuits for each strongly connected component by
Johnson’s Algorithm;

  4. 4.

compute the netting succession of circuits in order to maximize the total
clearing amount.

The first three steps involve algorithms which were covered substantially in
research papers ([18, 20, 12, 5]). In this paper, the above mentioned
algorithms are adapted for the netting problem. The third step, represented by
Johnson’s algorithm, is for the first time suggested as a possible computation
framework for an invoice netting problem in this paper. The fourth step
represents an innovative algorithmic solution for maximization of the total
clearing amount. We are aware of the fact that our paper does not use
groundbreaking algorithmic techniques. Nevertheless, we find it exciting when
modern daily life problems are solved using neat applications of classical
textbook algorithms.

The rest of the paper is organized as follows: In Section 2 we describe the
netting algorithms for our computational model and the implementation details.
Then, in Section 3 we present the results of our experiments based on data
provided by the Romanian Ministry of Economy. Finally, in Section 4 we present
conclusions and future research directions.

##  2 Netting algorithms

In this section we present details related to the proposed netting algorithms.
At first, we described the invoice graph representation and the strongly
connected components computation. Secondly, we describe the use of Johnson’s
algorithm for netting circuits computation. Finally, we present the algorithms
for netting amounts maximization.

###  2.1 Representing a directed graph based on invoice data and computing the
strongly connected components

A directed graph is an ordered pair $G=(V,E)$ (see [20] for basic graph
terminology). The set $V$ represents a set of vertices also known as nodes or
points. The set $E$ is defined as a set of ordered pairs of nodes, known also
as directed edges, arcs or directed lines. Considering the netting model, the
companies are represented as nodes in the graph. A payment obligation from a
company to another company is rendered as an edge in the graph. For example,
if company A issues a set of invoices to company B, an edge from B to A has
the total weight of the sum of invoices. One simple circuit (i.e., no vertices
nor edges can repeat) in the graph represents a set of companies for which a
netting can be implemented.

######  Definition 1 (Netting Problem)

The input of the problem is a directed graph G = (V, E), with a cost
$w:E\to\mathbb{R}$ associated to each edge. The operation of _settling_ a
circuit consists of decreasing the value of all the edges in the circuit with
the minimum value of an edge in that circuit. That is, given a circuit
$(v_{1},v_{2},\dots v_{k},v_{1})$, let $x$ be the minimum value of an edge in
the circuit, i.e., $min($$min_{i=1}^{k-1}w(v_{i},v_{i+1}),w(v_{k},v_{1}))$ by
replacing the weight for each edge $w(v_{i},v_{i+1})$ with
$w^{\prime}(v_{i},v_{i+1})=w(v_{i},v_{i+1})-x$, respectively
$w^{\prime}(v_{k},v_{1})=w(v_{k},v_{1})-x$.

The goal of the netting problem is to find an ordered set of circuits such
that settling them in the prescribed order maximizes the total netted amount.

According to [1], the netting problem defined above is NP-hard. Johnson’s
algorithm, as it is described in [12], represents a method of computation for
the all pairs shortest path problem considering a directed sparse graph. The
graph density $D$ is defined as $|D|=\frac{|E|}{|V|(|V|-1)}$.

Recall that, in our case, the nodes in the invoice graph are represented by
companies while the edges represent invoice relations between companies. In an
economy, a company interacts with a limited number of counterparties and this
gives us the intuition of why the invoice graph is a sparse one. Considering
the graph density formula, we made simulations on the invoice graphs created
from real data provided by Romanian Institute of Management and Informatics
and, indeed, we observe that the invoice graph is a sparse one.

Companies upload their invoices in the netting system. At a regular interval
the graph is updated, the circuits are computed and the companies are notified
about possible nettings. If all the companies in a netting circuit approve the
settlement, the sums are discarded from the graph. In this manner, the
companies diminish their mutual obligations. As an example, Figure 2 outlines
a netting scenario before and after netting implementation. Considering four
companies (A, B, C, D) as vertices, the liabilities between them are marked on
the edges. The minimum value of an edge in the ABCD circuit is 600 (the edge
between D and A). Therefore, a netting of 600 can be implemented between all
of these companies. After the netting implementation, 600 is subtracted from
the value of every edge. The liability of D for A becomes 0. The liabilities
marked on the edges AB, BC, CD have positive value, and can take part in other
netting circuits.

Figure 2: Netting implementation example

The first step in computing the netting circuits consists in identifying the
strongly connected components of the graph of invoices. The approach in this
paper is to consider Tarjan’s algorithm, which was firstly introduced in [18].
A directed graph is strongly connected if there is a path between all pairs of
vertices (see [20] for a formal definition). A strongly connected component
(SCC) of a directed graph is a maximal strongly connected subgraph. Because
the invoice graph is a sparse one, in order to efficiently determine the
circuits, we have to find first the strongly connected components of the
graph, and start the circuit computation on each of these components. In order
to determine the SCC, a choice had to be made between the Kosaraju’s algorithm
and Tarjan’s algorithm. As it is detailed in [18], considering the fact that
Kosaraju’s algorithm requires two DFS traversals of the graph, while Tarjan’s
algorithm involves only one DFS traversal, the latter one was considered. The
time complexity for Tarjan’s algorithm is $\mathcal{O}(|V|+|E|)$. Tarjan
algorithm is based on following ideas (see Algorithm 1 for a detailed
description):

  * •

a DFS tree/forest is obtained through a DFS search;

  * •

SCCs represent subtrees of the DFS tree;

  * •

starting from the head of a subtree, all the other nodes in the SCC can be
obtained;

  * •

there is no back edge from one SCC to another. (There can be cross edges, but
cross edges will not be used while processing the graph).

Algorithm 1 Tarjan’s algorithm for determining the strongly connected
components

1:function StrongConnect(vertex $V$)

2: $num\leftarrow num+1$

3: $order[V]\leftarrow num$

4: $link[V]\leftarrow order[V]$

5: push $V$ on the $Stack$

6: for $succesor$ in $vertexSuccesorsOfV$ do

7: if $order[succesor]$ is not defined then

8: StrongConnect($succesor$)

9: $link[succesor]\leftarrow min(link[V],link[succesor])$

10: else

11: if $V$ is on the $Stack$ then

12: $link[V]\leftarrow min(link[V],order[succesor])$

13: if $link[currentV]=order[currentV]$ then

14: Create a new strongly connected component

15: repeat

16: $auxVertex\leftarrow topOfStack$

17: add $auxVertex$ to strongly connected component

18: pop top from the $Stack$

19: until $currentV=auxVertex$

20:function TARJAN(graph $G$)

21: $num\leftarrow 0$

22: initialize $Stack$

23: for vertex $V$ in graph $G$ do

24: if $order[V]$ is undefined then

25: StrongConnect($V$)

###  2.2 Johnson’s algorithm for netting circuits computation

Johnson’s algorithm, first published in [12], is a method of computation of
all pairs shortest path problem in a directed sparse graph. Our problem
requires a particular approach for the Johnson’s algorithm, considering the
fact that all the weights are nonnegative. For the circuit enumeration problem
in directed sparse graphs, the solution proposed by Johnson consists in a
polynomial time algorithm. As Leiserson analyzed in [5], Johnson’s algorithm
is very similar to the Floyd-Warshall algorithm. In terms of efficiency,
Johnson’s algorithm time complexity is in direct dependency with the number of
arcs in a graph, as opposed to Floyd-Warshall, which has a different approach
(direct dependency with the number of nodes in a graph). This is the reason
why the algorithm developed by Donald B. Johnson is more suitable for sparse
graphs, while Floyd-Warshall is more effective on dense graphs. Johnson’s
algorithm runs in $\mathcal{O}(V^{2}\log{}V+|V||E|)$ time, while Floyd-Warshal
in $\mathcal{O}(V^{3})$. As Leiserson outlines in [5], Johnson’s algorithms is
based on two well known shortest path subroutines. The first one is Bellman-
Ford, used in order to eliminate negative edges and identify negative circuits
and to reweight the initial graph. The second one is Dijkstra’s shortest path
algorithm used to determine the shortest path between all pairs of nodes. In
our case, considering the fact that the value of edges can only be positive,
reflecting the sum of invoices, the Bellman-Ford step is not necessary.

Algorithm 2 Variation of Johnson’s algorithm for computing the netting
circuits

1:function CIRCUIT(vertex $V$)

2: $circuitFound\leftarrow false$

3: $maxNumberOfCircuitComponentsReached\leftarrow false$

4: push $V$ in the $stack$

5: $blockedVrtxList[V]\leftarrow true$

6: if $sizeOf(stack)\geq maxNumberOfCircuitComponents$ then

7: $maxNumberOfComponentsReached\leftarrow true$

8: else

9: for $vertexSuccesor$ in $succesorsOfV$ do

10: if $vertexSuccesor$ is $startVertex$ then

11: Save current circuit

12: $circuitFound\leftarrow true$

13: else

14: if $blockedVrtxList[vertexSuccesor]$ is false then

15: $circuitFound\leftarrow CIRCUIT(vertexSuccesor)$

16: if $circuitFound$ or $maxNumberOfCircuitComponentsReached$ then

17: UNBLOCK($V$);

18: else

19: for $vertexSuccesor$ in $succesorsOfCurrentVertex$ do

20: if $V$ is not in $blockedListForVertex$[$vertexSuccesor$] then

21: Add $V$ to $blockedListForVertex$[$vertexSuccesor$]

22: pop from the $stack$

23: return $circuitFound$

Algorithm 3 Unblock procedure

1:function Unblock(vertex $V$)

2: $blocked[V]\leftarrow true$

3: while $blockedListForVertex[V]$ is not empty do

4: $vertexToUnblock\leftarrow$ first element from $blockedListForVertex[V]$

5: if $vertexToUnblock$ is in $blockedVertexesList$ then

6: UNBLOCK($vertexToUnblock$)

In our variation of Johnson’s algorithm, at line 6 one can notice the use of
$maxNumberOfCircuitComponents$. This is the adaption for the netting problem
we made from the original Johnson’s algorithm. The circuit search is stopped
if the stack exceeds this threshold value. The idea is that a netting circuit
has to be approved by all of the members, in order to be effectively
implemented. The longer a circuit, the lower the probability of acceptance for
all the members. Therefore, the search is limited to a certain variable. In
order to set the value of the $maxNumberOfCircuitComponents$, a statistic is
realized for computing the most probable size of an implemented circuit.
Therefore, the variable is set as twice the value of the most probable circuit
length.

###  2.3 Maximize the netting implementation

The algorithms outlined in Subsection 2.1 and Subsection 2.2 present how the
netting circuits are computed. Once we have these circuits, another important
problem is to maximize the total netting implementation value. The
maximization can be realized by selecting a proper order for netting. For
example, Figure 3 outlines three netting circuits. If one firstly implements
circuit ABCD, a total amount of 28.000 ($7000\times 4$) is obtained. In this
situation, the second circuit ABDEF cannot be implemented, because the edge AB
would have a remaining value of 0. Moreover, the circuit BCGH cannot be
implemented, because the edge BC would have a remaining value of 0. However,
if the ABDEF circuit is implemented first, an amount of 1000 is generated
($200\times 5$). Thereafter, for the ABCD circuit an amount of $27\,200$ is
generated. Considering both circuits, ABDEF and ABCD, in this order or
implementation, a total amount of $28\,200$ is generated. In this case,
circuit BCGH cannot be implemented. Similarly, the edge BC would have a
remaining value of 0. The optimal implementation order is ABDEF, BCGH and
ABCD. This implementation results in a total amount of $29\,000$.

The aforementioned example is a simple one, considering just three circuits.
In real life, hundreds of thousands circuits have to placed in an optimal
implementation order. Even if in the previous example the total gain seems to
be a small one, in other situations the gain is significantly higher. We
describe an algorithm for circuit implementation optimization. Every circuit
computed in the previous section represents a vertex in a graph. In this
graph, an edge between two vertices represents the fact that the two circuits
have an intersection. The value of the edge is considered as the smallest
value of a segment in the intersection.

Therefore, if one considers vertex 1 and vertex 2, if the edge between them
has value 200, it means that the smallest intersection between the two
circuits is 200. Therefore, if a netting is implemented by using circuit 1,
and if the netting value per segment is 200, then the second circuit cannot be
implemented, because the segment of 200 is already consumed. However, if the
netting is implemented by using circuit 1, and if the netting value per
segment is 150, therefore the intersection between circuit 1 and circuit 2 is
reduced to 50. Therefore, considering circuit 2, the maximum amount which can
be considered in netting per segment is the minimum between 50 and the minimum
segment of circuit 2 outside of the intersection with circuit 1. This idea is
outlined by Figure 3, in which we have as nodes the previously presented
circuits, ABCD (with an amount of 7000 per edge), ABDEF (with an amount of 200
per edge), BCGH (with an amount of 300 per edge). As we previously mentioned,
the flow of algorithms is: create the invoice graph; compute the strongly
connected components; compute the circuits for every strongly connected
components; optimize the netting implementation order. In this optimization
phase, the algorithm runs on every set of circuits resulted from a strongly
connected component. More precisely, for every set of circuits resulted from a
strongly connected component, we select an arbitrary vertex $v$ and call
OptimizationAlgorithm on $v$ (see Algorithm 4). Algorithm 4 exhaustively tries
all the possible ordering of the circuits, which guarantees its optimality.

Algorithm 4 Circuit settlement optimization

1:function OptimizationAlgorithm(vertex $V$)

2: Add V to settlement solution

3: Eliminate from the graph all vertices which are excluded because of the
implementation of the $V$

4: if there are any nodes remaining in Graph then

5: for vertex $next$ in Graph do

6: OptimizationAlgorithm($next$)

7: else

8: Save the optimization solution and its value

9: Remove current node from the settlement solution

10: Reload into the graph the nodes excluded previously because of the
implementation of current node

Figure 3: Circuit settlement optimization example

##  3 Experiments

In this section we outline details regarding our experiments. Also, we present
several interesting implementation details. Our flow of algorithms has four
phases: directed graph creation, strongly connected components computation,
circuits determination, order of circuits implementation optimization. The
flow of algorithms was tested on raw data provided by the Institute of
Management and Informatics, Romanian Ministry of Economy. The algorithms were
implemented by using C# .NET Core 3.0, a Microsoft Technology. The hardware
involved in the experiments consisted in two Dell PowerEdge R730 Servers, with
128 GB of RAM.

We tested our algorithm on both real data provided by the Romanian Ministry of
Economy in order to compare our algorithms with the results achieved manually
the period 2000-2017. Moreover, we also use some simulated data which contains
much larger instances than the real ones. Thus, we aim to test the robustness
of our algorithm.

Then, in Figure 4, we outline an example of computation in which $15\,000$
companies are involved, with $50\,000$ distinct invoice paths between them. We
carried out several experiments, considering the computation of circuits
between 2 and 8 components. From the statistics provided by the Institute of
Management and Informatics, more than 90% of the nettings are realised by
circuits with maximum 4 components. In our simulations we have a circuit
length of maximum 8 components, double the size of the most probable circuit
length, which is 4. The running time for computing circuits of maximum 8
components is a feasible one for the practical application. As we observe from
the test data set of $15\,000$ companies and $50\,000$ distinct invoice paths,
computing circuits with more than 6 components conducts in a considerable
increase of computation time.

Figure 4: Experiment results.  Figure 5: Comparison between the amounts netted
by IMI in comparison with the results of applying the maximization algorithm
Figure 6: Graph for the number of circuits implemented by IMI, compared with
the number of circuits computed by the flow of algorithms for the invoices
implied by the implemented circuits

We compare in Figures 5 and 6 the number of netting circuits implemented by
IMI, Ministry of Economy with the number of circuits computed by the flow of
algorithms (first three phases: directed graph creation, strongly connected
components computation, circuits determination) for the invoices used in the
implemented nettings. In order to compute the number of circuits for every
year, we consider the invoices on which the real life nettings were realised
in that year. For example, in 2004, IMI implemented $49\,863$ nettings. Based
on the invoices which support these nettings our algorithms determine
$282\,727$ circuits. Notice that the total number of computed circuits is at
least five times the number of implemented nettings. Recall the fact that IMI
implemented circuits as a request from the business agents, based on their day
by day interaction, circuits not resulted from a method of computation.
Therefore, these figures outline the fact that by using the flow of algorithms
the set of netting solutions would increase significantly. Moreover, by
registering more and more invoices, the set of computed netting circuits would
increase considerably.

Figure 7: Graph for comparing the netting amounts realised by IMI, the results
of the maximization algorithm phase for the netting circuits implemented by
IMI, the results of the maximization algorithm phase for the netting computed
circuits

In Figures 5 and 7 we outline the results of applying the fourth step of the
algorithm flow (order of circuits implementation optimization) for the netting
circuits implemented by IMI, but also for the sets of computed circuits. One
can notice the fact that the sum of netted amount would have increased from
around 243 billion to around 397 billion if the proper order of implementation
would have been used for the nettings realised by IMI (the increase is more
than 60%). Moreover, if the computed circuits would have been implemented in
the proper order, a total amount of around 907 billion RON would have been
realised. The sum represents an increase of around 270% in comparison with the
amount of 243 billion implemented by IMI.

##  4 Conclusion

Clearing represents an important mechanism for improving the interactions
between the companies in an economy. It consists in an act of agreement in
which each party sets off amounts it owes against the amounts owed to it. In
this paper we presented a set of graph algorithms in order to compute netting
solutions at the economy scale of a country. The analysis and experiments are
realized based on real life data provided by the Romanian Ministry of Economy.

As future work, we aim to consider an additional type of optimization in order
to maximize the total number of participants in the netting process. In the
current paper we optimized the maximum netted amount. However, another helpful
aspect for the economy is to involve as many companies as possible in order to
benefit from the advantage offered by clearing. By maximizing the netting
amount, we noticed that in some cases smaller and medium sized companies which
interact with large ones are disadvantaged, because the proposed circuits tend
to advantage the larger companies in order to maximize the sums. We plan
design an optimization algorithm for balancing the netted amount and the
number of participants.

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# Empirical Investigation of Factors that Influence
Human Presence and Agency in Telepresence Robot

Nungduk Yun1 and Seiji Yamada2 1Nungduk Yun is with The Graduate University
for Advance Studies, SOKENDAI, Tokyo, Japan<EMAIL_ADDRESS>Seiji Yamada with
National Institute of Informatics, NII, Tokyo, Japan<EMAIL_ADDRESS>
###### Abstract

Nowadays, a community starts to find the need for human presence in an
alternative way, there has been tremendous research and development in
advancing telepresence robots. People tend to feel closer and more comfortable
with telepresence robots as many senses a human presence in robots. In
general, many people feel the sense of agency from the face of a robot, but
some telepresence robots without arm and body motions tend to give a sense of
human presence. It is important to identify and configure how the telepresence
robots affect a sense of presence and agency to people by including human face
and slight face and arm motions. Therefore, we carried out extensive research
via web-based experiment to determine the prototype that can result in
soothing human interaction with the robot. The experiments featured videos of
a telepresence robot (n = 128, $\textbf{2}\times\textbf{2}$ between-
participant study robot face factor: video-conference, robot-like face; arm
motion factor: moving vs. static) to investigate the factors significantly
affecting human presence and agency with the robot. We used two telepresence
robots: an affordable robot platform and a modified version for human
interaction enhancements. The findings suggest that participants feel agency
that is closer to human-likeness when the robot’s face was replaced with a
human’s face and without a motion. The robot’s motion invokes a feeling of
human presence whether the face is human or robot-like.

##  I INTRODUCTION

There is a wide variety of means of digital communication. For example, the
telephone, e-mail, SNS, and video conferencing are representative and the most
common. In recent years, communication via telepresence robots has been
attracting attention. Telepresence robots called “mobile robotic presence
systems,” that is physical robotic platforms with a video-conferencing system
mounted on a robotic mobile platform [1].Since remote operators can control
this physical embodiment which is telepresence robot in a remote location,
these systems chance to increase for video-conference and audio-communication
[1][2] and imbue communicators with a strong sense of presence [3]. Other
researchers have mentioned that telepresence robots provide a new
communication platform in various situations. For example, business,
education, and Medical related [4][5][6][7][8]. Furthermore, recently, these
robots have become a new platform for people with disabilities to use so that
they can join in society and perform labor [9].

In the field of telepresence robots, it is said that the visibility of a face
is a factor that makes people feel the presence of a person [3][8]. Previous
research on movement with telepresence robots has shown that robots that can
express themselves socially through movement are more immersive and desirable
than those that do not move [10]. In some cases, a robot that does not have a
human face can make people feel the presence of a person through its movements
[11]. For telepresence robots, the effect the face has depends on whether the
face is human-like or robot-like, and people may feel that one type gives a
greater sense of agency or presence. Also, which makes people feel more agency
or presence in a robot, the case with or without arm motion which is moving or
static?

In this paper, we conducted a web-based experiment featuring video of a
telepresence robot ($n$ = 128, $2\times 2$ between-participant study, robot
face factor: video-conference, robot-like face; arm motion: moving, static) to
investigate which factors significantly affect human presence and agency.

##  II related work

###  II-A Robots’ Facial Cues in HRI

One of the most important factors in human-robot interaction (HRI) is the
ability to show facial cues. In literature, McGinn conducted various studies
on service robots by changing their heads and facial cues to determine the
effect on social interface between human and robots. To facilitate better
communication between human and robot, it is common for robots to possess
head-like features that is capable of providing social feedback. Although it
is not a human’s face and expression, research has shown that relation between
human and the robot can be enhanced when the robot is equipped with human-like
“robotic” face that can express and show motion like humans [12]. In addition,
interaction with robot gets even better when the robot exhibits social
behaviors with anthropomorphic characteristics [13] [12].

Effect of human’s facial cue on robots were discussed in Mollahosseini et al.
[14]. The study indicated that eye gaze and certain facial expressions from
the actual human can further improve the relation between human and robots by
physically displaying human’s face on the 2D screen using telecommunication
either telepresence or a virtual agents [14]. For example, Beam is one of the
known telepresence robotic system that utilizes this method by replacing
robot’s head with the LED screen to display human’s face via video-conference.
Several research and surveys indicated that people can really feel the
presence of human in the robot [6][3].

###  II-B Non-verbal Cues in HRI

Previous research indicated that, non-verbal cues are becoming important
factors in HRI technology as it plays a significant role in human-human
interaction. Telepresence robot that has an ability to show social expression
by the motion movement can make user to feel engagement and likeable [10].
OriHime is one of the telepresence and avatar robot with human-like behavior
that was designed by Ory Laboratory Inc. The purpose of this technology is to
aid people to engage in life-like social behavior over distance, facilitate
human-to-human social interaction, and serve as an avatar to the user [15].
Although OriHime does not have an expressive facial cue, but its limb movement
and the voice from the user relaxes the social-relation between human and the
robot and still feel the presence of human in them [11]. In addition, having
social expression embodiment like Orhime-D can join society and social events
for disabled people and fulfill their mentality [9]. Spatial configuration and
body orientation of a telepresence robot affected people enable to arrange
themselves, robot tend to copy human-like action and theyt detected by the
surrounded motion [16]. This greatly increases interaction quality between
human and robots.

In the research using teleoperated robot with the Wizard of OZ method,
participants was not affected enjoyment by the knowledge of whether the robot
was being controlled by a program or a human [17]. Yamada et al. proposed
motion-based ASE(Artificial Subtle Expressions) in which a robot slowly
hesitates by turning to a human before giving advice with low confidence. As
they conclude, the long or short-wait expressions might be applicable to
expressing a robot’s confidence, fast or slow-motion as a motion-ASE is more
suitable for such expressions [18]. The other research suggest that
synchronized on-screen and in-space gestures significantly improved
viewers(participants)’ interpretation of the action compared to on-screen or
in-space gestures alone and addition of proxy motion also improved measures of
perceived collaboration [19]. Furthermore, in-space gestures positively
influenced perceptions of both local and remote participants [19].

##  III Platform

We used a humanoid robot, Rapiro [20], which is widely used for different
applications, such as for education and hobbies[21][22]. The Arduino and
Raspberry Pi boards in the robot enable users (developers) to communicate with
the robot by only sending command signals from a PC, and they also allow for
the system to be extended easily. Therefore, we used this robot as a
telepresence robot for our experiment.

For the experiment, we fixed Rapiro’s eye color to blue due to color bias. We
modified Rapiro’s head as a prototype for experimental study and to show the
remote user’s face.

###  III-A Hardware Spec

Rapiro 111http://www.rapiro.com/ has 12 degrees of freedom (DoF), a USB
camera, a microphone in its forehead, and a speaker inside of its head. Fig. 4
shows an overview of Rapiro.

Modifications to Rapiro, we modified the head of another Rapiro to show the
face of a remote user. We used a 5-inch portable monitor, and the head was
made of PLA using a 3D printer. This Rapiro also had 12 DoF, a USB camera,
microphone, and speaker inside of its head. Fig. 4 shows an overview of the
modified Rapiro.

###  III-B User Interface and Robot Motion

To control Rapiro, we made a keyboard input interface. When the operator (from
a geographically separate location) presses the number “2” on the keyboard, a
local PC receives the signal from the operator’s location via Wi-Fi, and the
robot makes that specific motion.

We generated robot motions in accordance with the following principle. For
both of the robots, we used preset motions and the original motion which we
developed for the experiments, such as “hands up” and “wave the both hands”and
etc. In total, we used six motions in the video task and motions list showed
in Table I . The preset motions included motion like going forward or
backward, but we did not use these at this time.

TABLE I: List of Motions | Motion
---|---
1 | Both hands up
2 | Wave the both hands
3 | Stretch our right hand
4 | Grip both hands
5 | Left hand up
6 | Fluttering both hands

##  IV Experiment

###  IV-A Experimental Design

We conducted the experiment using a $2\times 2$ (robot face: video-conference
vs. robot-like face; arm motion: moving vs. static) between-participant
design. To explore how people interact widely with our design, we used G*Power
[23] sample size calculation (n =128), and we ran our experiment using online
questionnaire surveys along with showing the video. Participants were
recruited from the Yahoo! Crowdsourcing service and after finished experiments
we used Gooogle form for survey. For most of the methods for the online
experiment, we referred to Sirkin et al. [19]. We wanted the remote operator’s
speech and gestures to have precise timings and the same interaction content.
While online responses may differ from in-person experiments, from Powers et
al. [24], it was found that remote robots could be used in experiments and be
more sociable and engaging than co-located robots [24]. Furthermore, studies
comparing live and video-based HRI trials were both broadly equivalent in most
cases [25]. Therefore, we chose to run the experiment online. Our dependent
values were presence and agency. We designed the online experiment so that we
could compare which condition affect from our dependent values and perceptions
of the remote operator who communicated with them via the telepresence robot
across four robot conditions:

  1. 1.

Human face and moving: The face of the robot used a video-conference style
screen from which the remote operator was shown, and the robot’s arm made
motions. An overview of this robot is shown in Fig. 4.

  2. 2.

Human face and Static: The face of the robot used a video-conference style
screen from which the remote operator was shown, and the robot’s arm was
static. An overview is shown in Fig. 4.

  3. 3.

Robot face and moving: The face of the robot was robot-like, and the robot’s
arm made motions. An overview is shown in Fig. 4.

  4. 4.

Robot face and Static: The face of the robot was robot-like, and the robot’s
arm was static. An overview is shown in Fig. 4.

Figure 1: Human face and Moving. Figure 2: Human face and Static.
---
Figure 3: Robot face and Moving. Figure 4: Robot face and Static.

###  IV-B Hypotheses

We formulated four hypotheses for our experiment. As mentioned above, we
conducted the experiment using a between-participant design (robot face:
video-conference vs. robot-like face; arm motion: moving vs. static) to
investigate which factors significantly affect presence and agency.

  * •

H1 Face affects agency.

  * •

H2 Motion affects agency.

  * •

H3 Face affects presence.

  * •

H4 Motion affects presence.

###  IV-C Participants

A total of 216 participants took part in the experiment online (male: 147,
female: 69). Their ages ranged from 18 to 63 (M = 44.2, SD = 10.6). We
recruited the participants from Yahoo! Crowdsourcing, which is a service
provided by Yahoo! Japan.

###  IV-D Task

The participants watched one video from among the four different conditions as
shown in Fig.1,2,3,4. We created videos in which a remote operator
communicated via a telepresence robot and discussed moon survival and item
ranking. We created this Moon Survival scenario from the Desert Survival
Problem [26] and also a NASA exercise [27] since the Desert Survival Problem
is used by many social scientists and robotics researchers [10][28][8][2][29].
The video was about an astronaut who had crash-landed on the moon and was
discussing how to select 5 items that he needed from the 15 items left to
return to his distant home planet. Due to the video length, we only discussed
ranking up to five items because if we had gone up to 15 items, the video
length would have been too long. The ranking of the five items is shown in the
Table II.

TABLE II: Rank of Items | experimenter | Remote operator
---|---|---
1 | Tanks of oxygen | Tanks of oxygen
2 | Map of the Moon’s surface | Water
3 | Nylon rope | Food concentrate
4 | Parachute | First aid kit
5 | Life raft | Map of the Moon’s surface

###  IV-E Procedure

The procedure is shown in Fig. 5. The participants viewed the instructions and
watched one video from the four conditions. In the instructions, we stated
that, “In the experiment, you will watch a video of a human talking to a robot
controlled by a human via remote control” and “Watch as if you were talking to
the robot.” Afterward, we also told them that the task of the video was to
have a discussion on moon survival. When participants finished watching the
video, they were asked to rate their agreement on a seven-point Likert scale,
1 = strongly disagree, 7 = strongly agree, in two questionnaire surveys (in
total, 30 statements). When they finished the experiment, there was an
additional comment or question space. We paid 100 yen (about $1.00US), and the
average time to complete the study was about 15 to 30 minutes.

Figure 5: Flowchart of experiment

###  IV-F Questionnaire Survey

We used two different questionnaires, the Godspeed series and one for social
presence. Godspeed is a standardized measurement tool for HRI [30]. There are
five key concepts for the measurement used: anthropomorphism, animacy,
likeability, perceived intelligence, and perceived safety. For the second
questionnaire, we used Networked Minds Measure of Social Presence, which is
measure of presence [28]. We modified this questionnaire due to some of the
statements not fitting into our experiment. A few of the questions from the
first and second questionnaires are listed in Tables 1 and 2.

TABLE III: GODSPEED’s Questionnaire | ANTHROPOMORPHISM |
---|---|---
1 | Fake | Natural
2 | Machinelike | Humanlike
3 | Unconscious | Conscious
4 | Artificial | Lifelike
5 | Moving rigidly | Moving elegantly
TABLE IV: Networked Minds Measure of Social Presence’s Questionnaire | Social Presence |  |
---|---|---|---
1 | I often felt as if I was all alone |  |
2 | I think the other individual often felt alone. |  |
3 | I was often aware of others in the environment. |  |
4 | Others were often aware of me in the room. |  |
5 | The other individual paid close attention to me |  |
6 | I paid close attention to the other individual. |  |
7 | The other individual tended to ignore me. |  |
8 | My behavior was in direct response to the other’s behavior. |  |
9 | etc.. |  |

##  V result

To test our hypotheses, we used a two way analysis of variance (ANOVA). For
the G*Power calculation [23], the sampling size was 128. For each condition,
we used 32 participants for analysis.

Before participants watched a video, they were asked to rate their agreement
on a seven-point Likert scale, 1 = not very familiar, 7 = very familiar, for
two statements (“Are you familiar with video conferences?” and “Are you
familiar with robots?”). Most participants were not familiar with robots (mean
= 2.46, SD = 1.57 ), but they were familiar with video conferences (mean =
3.39, SD = 1.84). We used anthropomorphism from the GODSPEED questionnaire
series to measure agency [30]. To measure presence, we used Networked Minds
Measure of Social Presence’s questionnaire [28].

###  V-A Meausrement

The results of the ANOVA showed in Table IX and Table VIII, also result of
simple mian effect for agency showed in Table X. As well as the means and
standard deviations(S.D.) for all of the dependent variables can be seen in
Figs. 6 and 7 as well as in Table VI and Table VII. Also, conditions explain
again in Table V. For agency, we found that the interaction was significant(p
<0.01). In the Static group, the simple main effect of face was significant(p
<0.0001). It was higher in the group with face. For presence, there was a
significant interaction between the two factors. We found that the main effect
was significant only for the motion factor(p <0.01). Furthermore, motion with
moving was the highest.

Figure 6: Averages for score for motion perceived for each condition in experiment. Anthropomorphism as dependent value. Figure 7: Averages for score for motion perceived for each condition in experiment. Presence as dependent value. TABLE V: Conditions in the experiments condition | Face | Motion
---|---|---
condition1 | Human Face | Moving
condition2 | Human Face | Static
condition3 | Robot Face | Moving
condition4 | Robot Face | Static
TABLE VI: Agency of S.D. and Mean Condition | MEAN | S.D.
---|---|---
condition1 | 3.05 | 0.92
condition2 | 3.57 | 1.34
condition3 | 2.98 | 0.91
condition4 | 2.51 | 1.08
TABLE VII: Presence of S.D. and Mean Condition | MEAN | S.D.
---|---|---
condition1 | 4.08 | 0.54
condition2 | 3.91 | 0.42
condition3 | 4.03 | 0.52
condition4 | 3.66 | 0.67
TABLE VIII: RESULT OF TWO-WAY ANOVA FOR Presence

Source | F(1,124) | p |
---|---|---|---
Face | 2.457 | 0.119 | n.s.
Motion | 8.144 | 0.005 | **
Interaction | 1.00 | 0.316 | n.s.

  * *

*p <.05,**p <0.01

TABLE IX: RESULT OF TWO-WAY ANOVA FOR Agency

Source | F(1,124) | p |
---|---|---|---
Face | 8.776 | 0.003 | **
Motion | 0.021 | 0.883 | n.s.
Interaction | 6.772 | 0.010 | *

  * *

*p <.05,**p <0.01

TABLE X: RESULT OF SIMPLE MAIN EFFECT TEST FOR Agency

Simple Main Effect | F(1,124) | p |
---|---|---|---
Face (Moving) | 0.0648 | 0.7994 | n.s.
Face (Static) | 15.4846 | 0.0001 | ***
Motion (Human Face) | 3.7806 | 0.0541 | n.s.
Motion (Robot Face) | 3.0139 | 0.0850 | n.s.

  * *

*p <.05,**p <0.01,***p <0.001

##  VI Discussion

###  VI-A Hypotheses Summary

The first section in the Experiment section set four hypotheses for what we
expected to be the outcome of the experiment. Here are the results:

  * •

H1 Face affects agency: In the Static group, a simple main effect was found
for the face factor (p <0.0001), which was partially supported.

  * •

H2 Motion affects agency: This hypothesis did not hold since a simple main
effect was not found for the motion factor.

  * •

H3 Face affects presence: This hypothesis did not hold since there was no main
effect of the face factor on presence.

  * •

H4 Motion affects presence: This hypothesis held since a main effect on
presence was found for the motion factor (p <0.01).

When the telepresence robot had a Human Face and no arm motion which is
Static, the participants felt the robot to be human-like. Since a real human’s
face could be seen, they felt this robot to be most human-like. Even when the
human’s face appeared with motion which is moving, the participants did not
feel the robot to be not human-like. Regarding the presence factor,
participants felt presence when there was robot do motions since main effect
on presence factor (p <0.01). So, it doesn’t matter with between the human
face and robot-like face by reason of no main effect on face factor.

From additional comments and questions from the survey, several participants
mentioned that it was difficult to watch the video and answer questions
because the motors were too loud, but there was no problem with the motions.

###  VI-B Generality and Limitation

There are certain generalities and the study presented here has limitations
that may affected the generalities of our result. First, our use of a Rapiro
as robot platform might affect generality since we only tested this with a
particular two robots. Naturally, each type of robot embodiments had own
limitations due to number of actuators. However, the finding of robot
embodiment could not necessarily be generalized to other types of robotic
embodiments [14]. Second, the lack of support for hypotheses in motion what we
developed robot’s motion which used in experiments and motion lists showed in
Table I. In addition, the delay between remote operator’s speaking and motion
playback speed also type of motion might affect perceptions of the presence
and agency.

Third, Robot face may affected generality. We already mention above, the
finding of robot embodiment could not necessarily be generalized to other
types of robotic embodiments [14] and we believed also same as facial cue. In
the other hand, Japanese people often imagine humanoid robots as friendly
[17], since we only used Japanese participants, unsure about people in other
culture can be applied in our results.

Regarding online experiments in general, Crump et al. [31] showed that the
data collected online using a web-browser seemed mostly in line with
laboratory results, so long as the experimental methods were solid.

There were problems with the human-likeness and machine-likeness from the
video task. When the face was robot-like, for even those participants not used
to robots, the robot appeared human-like, and the way the robot talked sounded
human-like. When the face was that of a human, the participants felt the robot
to be uncanny because it had a human face but a robot body. This may relate to
the uncanny valley. Furthermore, most participants felt as if they were having
a video chat for the condition using a Human Face without arm motion which is
Static. In future work, we will conduct in-person experiment same conditions
and method in this study. Also, we will compare between video chat and this
condition of using a human face and no motion.

Last, we found that no matter which robot we used, even simple motions could
invoke a feeling of presence. Regarding human-face conditions, there was no
significant effect of gender in Sirkin et al. [19]. The design of future
telepresence robots will change depending on whether the emphasis is on human
likeness or presence.

##  VII CONCLUSIONS

In prior research, Non-verbal behaviors and facial cues are interesting and
essential cues in robot and computer-mediated communication. The present study
showed that individuals study that non-verbal behavior and facial cue in the
telepresence robot’s study. The result from this study advances our
understanding role of the nonverbal and facial cues in robot-mediated
communication.

In this study, we conducted $2\times 2$ between-participant experiment(robot
face: video-conference, robot-like face; arm motion: move, static). The result
showed that people felt a presence at motion factor even though doesn’t matter
with the human face and robot-like face. Furthermore, anthropomorphism as the
agency, people felt more in human face with static which is more human-like
than other conditions.

A comparison that only video-conference and human face embodiment with moving
or static will be future work for us. While the quality of communication
through embodied web-based experiment may never same as in-person experiment,
however our study facial and motion cue could support and helped social
interaction using a telepresence robot.

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