Privacy-Preserving Tabu Search for Distributed Graph Coloring

Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some fashion. The typical approach is to collect all of this information together and centrally solve the problem. However, this requires all parties to completely share their information, which may lead to serious privacy issues. Privacy-preserving techniques need to be developed to enable distributed optimization with limited information disclosure. A further complicating factor is that combinatorial optimization problems are typically NP-hard, requiring approximation algorithms or heuristics to provide a practical solution. In this paper, we focus on a very well known hard problem - the distributed graph coloring problem, which has been utilized to model many practical problems in scheduling and resource allocation. We propose an efficient protocol that securely solves this problem based on the tabu search metaheuristic. Specifically, our solution uses a distributed local search algorithm to find a good solution. We analyze the security of our approach and experimentally demonstrate the effectiveness of our approach.