Ziessler, Surana, Speranzon, Klus, Dellnitz, and Banaszuk have all served as co-authors in my efforts in this area. However, my extensive discussions with Prof. Michael Dellnitz inspired me to delve deeper into the area of dynamical systems and the analysis of algorithms!

Novel algorithm construction: decentralized graph clustering {#sec:graph}
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[Overview]{} Algorithms for graph analysis have a wide variety of applications such as routing, pattern recognition, database searches, network layout, and Internet PageRank to name a few [@Cit:graph_algos]. Although some of these problems can solved efficiently on present day computing devices, several graph analysis problems are computationally intractable [@Cit:cormen]. For example, the problem of partitioning graphs into equal size sets while minimizing the weights of cut edges arises in a range of settings such as social anthropology, gene networks, protein sequences, sensor networks, computer graphics, and Internet routing algorithms [@Cit:cluster2]. To avoid unbalanced cuts, size restrictions are typically placed on the clusters; instead of minimizing inter-connection strength, if one minimizes the ratio of the inter-connection strength to the size of individual clusters, the problem becomes NP-complete [@Cit:tutorial; @Cit:npcomp].

In [@Cit:cluster1; @Cit:cluster2], a novel decentralized algorithm for clustering/partitioning graphs that exploits fundamental properties of a dynamically evolving networked system was constructed. 