Detecting diamond necklaces in labeled dags (a problem from distributed debugging)

Abstract

The problem tackled in this paper originates from the debugging of distributed applications. Execution of such an application can be modeled as a partially ordered set of process states. The debugging of control flows (sequences of process states) of these executions is based on the satisfaction of predicates by process states. A process state that satisfies a predicate inherits its label. It follows that, in this context, a distributed execution is a labeled directed acyclic graph (dag for short). Debug or determine if control flows of a distributed execution satisfy some property amounts to test if the labeled dag includes some pattern defined on predicate labels. This paper first introduces a general pattern (called diamond necklace) which includes classical patterns encountered in distributed debugging. Then an efficient polynomial time algorithm detecting such patterns in a labeled dag is presented. To be easily adapted to an on-the-fly detection of the pattern in distributed executions, the algorithm visits the nodes of the graph according to a topological sort strategy.