Heuristics for Hierarchical Partitioning with Application to Model Checking

Abstract

Given a collection of connected components, it is often desired to cluster together<br />parts of strong correspondence, yielding a hierarchical structure. We address the <br />automation of this process and apply heuristics to battle the combinatorial and <br />computational complexity.<br />We define a cost function that captures the quality of a structure relative to the<br />connections and favors shallow structures with a low degree of branching. Finding<br />a structure with minimal cost is shown to be NP-complete. We present a greedy<br />polynomial-time algorithm that creates an approximate good solution incrementally<br />by local evaluation of a heuristic function. We compare some simple heuristic <br />functions and argue for one based on four criteria: The number of enclosed connections,<br />the number of components, the number of touched connections and the depth of the structure.<br />We report on an application in the context of formal verication, where our <br />algorithm serves as a preprocessor for a temporal scaling technique, called \"ext" heuristic<br /> [AW99]. The latter is applicable in enumerative reachability analysis and is included<br />in the recent version of the Mocha model checking tool.<br />We demonstrate performance and benefits of our method and use an asynchronous<br />parity computer, a standard leader election algorithm, and an opinion poll protocol as<br />case studies.