Heuristics for Hierarchical Partitioning with Application to Model Checking

M. Oliver Möller
Rajeev Alur

August 2000


Given a collection of connected components, it is often desired to cluster together parts of strong correspondence, yielding a hierarchical structure. We address the automation of this process and apply heuristics to battle the combinatorial and computational complexity. We define a cost function that captures the quality of a structure relative to the connections and favors shallow structures with a low degree of branching. Finding a structure with minimal cost is shown to be $NP$-complete. We present a greedy polynomial-time algorithm that creates an approximative good solution incrementally by local evaluation of a heuristic function. We compare some simple heuristic functions and argue for one based on four criteria: The number of enclosed connections, the number of components, the number of touched connections and the depth of the structure. We report on an application in the context of formal verification, where our algorithm serves as a preprocessor for a temporal scaling technique, called ``Next'' heuristic. The latter is applicable in enumerative reachability analysis and is included in the recent version of the MOCHA model checking tool. We demonstrate performance and benefits of our method and use an asynchronous parity computer, a standard leader election algorithm, and an opinion poll protocol as case studies

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