I've completed a paper design for the reimplementation of DeadLockCheck.
Notes attached, in case anyone wants to kibitz.  (This will appear in
storage/lmgr/README when I commit the code.)

			regards, tom lane


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The deadlock detection algorithm:

Since we allow user transactions to request locks in any order, deadlock
is possible.  We use a deadlock detection/breaking algorithm that is
fairly standard in essence, but there are many special considerations
needed to deal with Postgres' generalized locking model.

A key design consideration is that we want to make routine operations
(lock grant and release) run quickly when there is no deadlock, and avoid
the overhead of deadlock handling as much as possible.  We do this using
an "optimistic waiting" approach: if a process cannot acquire the lock
it wants immediately, it goes to sleep without any deadlock check.  But
it also sets a delay timer, with a delay of DeadlockTimeout milliseconds
(typically set to one second).  If the delay expires before the process is
granted the lock it wants, it runs the deadlock detection/breaking code.
Normally this code will determine that there is no deadlock condition,
and then the process will go back to sleep and wait quietly until it is
granted the lock.  But if a deadlock condition does exist, it will be
resolved, usually by aborting the detecting process' transaction.  In this
way, we avoid deadlock handling overhead whenever the wait time for a lock
is less than DeadlockTimeout, while not imposing an unreasonable delay of
detection when there is an error.

Lock acquisition (routines LockAcquire and ProcSleep) follows these rules:

1. A lock request is granted immediately if it does not conflict with any
existing or waiting lock request, or if the process already holds an
instance of the same lock type (eg, there's no penalty to acquire a read
lock twice).  Note that a process never conflicts with itself, eg one can
obtain read lock when one already holds exclusive lock.

2. Otherwise the process joins the lock's wait queue.  Normally it will be
added to the end of the queue, but there is an exception: if the process
already holds locks on this same lockable object that conflict with the
request of any pending waiter, then the process will be inserted in the
wait queue just ahead of the first such waiter.  (If we did not make this
check, the deadlock detection code would adjust the queue order to resolve
the conflict, but it's relatively cheap to make the check in ProcSleep and
avoid a deadlock timeout delay in this case.)  Note special case: if the
process holds locks that conflict with the first waiter, so that it would
go at the front of the queue, and its request does not conflict with the
already-granted locks, then the process will be granted the lock without
going to sleep at all.

When a lock is released, the lock release routine (ProcLockWakeup) scans
the lock object's wait queue.  Each waiter is awoken if (a) its request
does not conflict with already-granted locks, and (b) its request does
not conflict with the requests of prior un-wakable waiters.  Rule (b)
ensures that conflicting requests are granted in order of arrival.
There are cases where a later waiter must be allowed to go in front of
conflicting earlier waiters to avoid deadlock, but it is not
ProcLockWakeup's responsibility to recognize these cases; instead, the
deadlock detection code re-orders the wait queue when necessary.

To perform deadlock checking, we use the standard method of viewing the
various processes as nodes in a directed graph (the waits-for graph or
WFG).  There is a graph edge leading from process A to process B if A
waits for B, ie, A is waiting for some lock and B holds a conflicting
lock.  There is a deadlock condition if and only if the WFG contains
a cycle.  We detect cycles by searching outward along waits-for edges
to see if we return to our starting point.  There are three possible
outcomes:

1. All outgoing paths terminate at a running process (which has no
outgoing edge).

2. A deadlock is detected by looping back to the start point.  We resolve
such a deadlock by canceling the start point's lock request and reporting
an error in that transaction, which normally leads to transaction abort
and release of that transaction's held locks.  Note that it's sufficient
to cancel one request to remove the cycle; we don't need to kill all the
transactions involved.

3. Some path(s) loop back to a node other than the start point.  This
indicates a deadlock, but one that does not involve our starting process.
We ignore this condition on the grounds that resolving such a deadlock
is the responsibility of the processes involved --- killing our start-
point process would not resolve the deadlock.  So, cases 1 and 3 both
report "no deadlock".

Postgres' situation is a little more complex than the standard discussion
of deadlock detection, for two reasons:

1. A process can be waiting for more than one other process, since there
might be multiple holders of (nonconflicting) lock types that all conflict
with the waiter's request.  This creates no real difficulty however; we
simply need to be prepared to trace more than one outgoing edge.

2. If a process A is behind a process B in some lock's wait queue, and
their requested locks conflict, then we must say that A waits for B, since
ProcLockWakeup will never awaken A before B.  This creates additional
edges in the WFG.  We call these "soft" edges, as opposed to the "hard"
edges induced by locks already held.  Note that if B already holds any
locks conflicting with A's request, then their relationship is a hard edge
not a soft edge.

A "soft" block, or wait-priority block, has the same potential for
inducing deadlock as a hard block.  However, we may be able to resolve
a soft block without aborting the transactions involved: we can instead
rearrange the order of the wait queue.  This rearrangement reverses the
direction of the soft edge between two processes with conflicting requests
whose queue order is reversed.  If we can find a rearrangement that
eliminates a cycle without creating new ones, then we can avoid an abort.
Checking for such possible rearrangements is the trickiest part of the
algorithm.

The workhorse of the deadlock detector is a routine FindLockCycle() which
is given a starting point process (which must be a waiting process).
It recursively scans outwards across waits-for edges as discussed above.
If it finds no cycle involving the start point, it returns "false".
(As discussed above, we can ignore cycles not involving the start point.)
When such a cycle is found, FindLockCycle() returns "true", and as it
unwinds it also builds a list of any "soft" edges involved in the cycle.
If the resulting list is empty then there is a hard deadlock and the
configuration cannot succeed.  However, if the list is not empty, then
reversing any one of the listed edges through wait-queue rearrangement
will eliminate that cycle.  Since such a reversal might create cycles
elsewhere, we may need to try every possibility.  Therefore, we need to
be able to invoke FindLockCycle() on hypothetical configurations (wait
orders) as well as the current real order.

The easiest way to handle this seems to be to have a lookaside table that
shows the proposed new queue order for each wait queue that we are
considering rearranging.  This table is passed to FindLockCycle, and it
believes the given queue order rather than the "real" order for each lock
that has an entry in the lookaside table.

We build a proposed new queue order by doing a "topological sort" of the
existing entries.  Each soft edge that we are currently considering
reversing is a property of the partial order that the topological sort
has to enforce.  We must use a sort method that preserves the input
ordering as much as possible, so as not to gratuituously break arrival
order for processes not involved in a deadlock.  (This is not true of the
tsort method shown in Knuth, for example, but it's easily done by a simple
doubly-nested-loop method that emits the first legal candidate at each
step.  Fortunately, we don't need a highly efficient sort algorithm, since
the number of partial order constraints is not likely to be large.)  Note
that failure of the topological sort tells us we have conflicting ordering
constraints, and therefore that the last-added soft edge reversal
conflicts with a prior edge reversal.  We need to detect this case to
avoid an infinite loop in the case where no possible rearrangement will
work: otherwise, we might try a reversal, find that it still leads to
a cycle, then try to un-reverse the reversal while trying to get rid of
that cycle, etc etc.  Topological sort failure tells us the un-reversal
is not a legitimate move in this context.

So, the basic step in our rearrangement method is to take a list of
soft edges in a cycle (as returned by FindLockCycle()) and successively
try the reversal of each one as a topological-sort constraint added to
whatever constraints we are already considering.  We recursively search
through all such sets of constraints to see if any one eliminates all
the deadlock cycles at once.  Although this might seem impossibly
inefficient, it shouldn't be a big problem in practice, because there
will normally be very few, and not very large, deadlock cycles --- if
any at all.  So the combinatorial inefficiency isn't going to hurt us.
Besides, it's better to spend some time to guarantee that we've checked
all possible escape routes than to abort a transaction when we didn't
really have to.

Each edge reversal constraint can be viewed as requesting that the waiting
process A be moved to before the blocking process B in the wait queue they
are both in.  This action will reverse the desired soft edge, as well as
any other soft edges between A and other processes it is advanced over.
No other edges will be affected (note this is actually a constraint on our
topological sort method to not re-order the queue more than necessary.)
Therefore, we can be sure we have not created any new deadlock cycles if
neither FindLockCycle(A) nor FindLockCycle(B) discovers any cycle.  Given
the above-defined behavior of FindLockCycle, each of these searches is
necessary as well as sufficient, since FindLockCycle starting at the
original start point will not complain about cycles that include A or B
but not the original start point.

In short then, a proposed rearrangement of the wait queue(s) is determined
by one or more broken soft edges A->B, fully specified by the output of
topological sorts of each wait queue involved, and then tested by invoking
FindLockCycle() starting at the original start point as well as each of
the mentioned processes (A's and B's).  If none of the tests detect a
cycle, then we have a valid configuration and can implement it by
reordering the wait queues per the sort outputs (and then applying
ProcLockWakeup on each reordered queue, in case a waiter has become wakable).
If any test detects a soft cycle, we can try to resolve it by adding each
soft link in that cycle, in turn, to the proposed rearrangement list.
This is repeated recursively until we either find a workable rearrangement
or determine that none exists.  In the latter case, the outer level
resolves the deadlock by aborting the original start-point transaction.

The particular order in which rearrangements are tried depends on the
order FindLockCycle() happens to scan in, so if there are multiple
workable rearrangements of the wait queues, then it is unspecified which
one will be chosen.  What's more important is that we guarantee to try
every queue rearrangement that could lead to success.  (For example,
if we have A before B before C and the needed order constraints are
C before A and B before C, we would first discover that A before C
doesn't work and try the rearrangement C before A before B.  This would
eventually lead to the discovery of the additional constraint B before C.)

Got that?

Miscellaneous notes:

1. It is easily proven that no deadlock will be missed due to our
asynchronous invocation of deadlock checking.  A deadlock cycle in the WFG
is formed when the last edge in the cycle is added; therefore the last
process in the cycle to wait (the one from which that edge is outgoing) is
certain to detect and resolve the cycle when it later runs HandleDeadLock.
This holds even if that edge addition created multiple cycles; the process
may indeed abort without ever noticing those additional cycles, but we
don't particularly care.  The only other possible creation of deadlocks is
during deadlock resolution's rearrangement of wait queues, and we already
saw that that algorithm will prove that it creates no new deadlocks before
it attempts to actually execute any rearrangement.

2. It is not certain that a deadlock will be resolved by aborting the
last-to-wait process.  If earlier waiters in the cycle have not yet run
HandleDeadLock, then the first one to do so will be the victim.

3. No live (wakable) process can be missed by ProcLockWakeup, since it
examines every member of the wait queue (this was not true in the 7.0
implementation, BTW).  Therefore, if ProcLockWakeup is always invoked
after a lock is released or a wait queue is rearranged, there can be no
failure to wake a wakable process.  One should also note that
LockWaitCancel (abort a waiter due to outside factors) must run
ProcLockWakeup, in case the cancelled waiter was soft-blocking other
waiters.

4. We can minimize excess rearrangement-trial work by being careful to scan
the wait queue from the front when looking for soft edges.  For example,
if we have queue order A,B,C and C has deadlock conflicts with both A and B,
we want to generate the "C before A" constraint first, rather than wasting
time with "C before B", which won't move C far enough up.  So we look for
soft edges outgoing from C starting at the front of the wait queue.

5. The working data structures needed by the deadlock detection code can
be proven not to need more than MAXBACKENDS entries.  Therefore the
working storage can be statically allocated instead of depending on
palloc().  This is a good thing, since if the deadlock detector could
fail for extraneous reasons, all the above safety proofs fall down.

Thu, 18 Jan 2001 20:20:05 -0500
Tom Lane <tgl@sss.pgh.pa.us>
Deadlock reimplementation notes (kinda long)