Formal Modeling and Verification of a Distributed Algorithm for Constructing Maximal Cliques in Static Networks

Abstract

Constructing maximal cliques is a well-known problem in the graph theory. Despite this problemhas been well studied for decades, few efforts have been presented in distributed computing. The main contribution of this paper is to propose a distributed algorithm, modeled by local computations, for constructing all maximal and disjoint cliques in astatic network. In order to prove the correctness of this algorithm, we use the formal Event-B method, which is based on the refinement technique. The latter consistsin enriching a model in a step by step fashion. It is the foundation of the correct by construction approach which provides an easy way to prove algorithms.