  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. A typical approach for solving such problem 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. Thus, it is desirable to propose a privacy preserving
technique that can securely solve specific combinatorial optimization problems.
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 real world problems in scheduling and resource allocation. We propose
efficient protocols to securely solve such fundamental problem. We analyze the
security of our approach and experimentally demonstrate the effectiveness of
our approach.
