Summary: Heuristics for Hierarchical Partitioning
with Application to Model Checking ?
M. Oliver M¨oller 1 and Rajeev Alur 2
1) BRICS ?? 2) University of Pennsylvania
Department of Computer Science Computer & Information Science
University of Aarhus Moore building
Ny Munkegade, building 540 200 South 33rd Street
DK 8000 š Arhus C, Denmark Philadelphia, PA 19104, USA
Fax.: (+45) 8942 3255 Fax.: (+1) 215 8980587
Abstract. 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
NP complete. We present a greedy polynomialtime algorithm that approximates good solutions in
crementally by local evaluation of a heuristic function. We argue for a heuristic function 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