Certification of Distributed Algorithms Solving Problems with Optimal Substructure

Abstract

We report work-in-progress on applying the concept of a certifying algorithm to distributed algorithms. A certifying algorithm produces not only a result, but also a witness that verifies the result’s correctness. Certifying variants of numerous (sequential) algorithms have been developed. However, distributed algorithms behave differently from sequential algorithms. Consequently, it is challenging to make them certifying. Our local approach is to make the distributed algorithm compute many local witnesses that together verify the result’s correctness. We identified problems for which this approach is applicable. Particularly, we hypothesize that for problems with optimal substructure (i.e., an optimal solution can be constructed from optimal solutions of its subproblems) it is often easy to apply the local approach. As an example, we give a certifying distributed algorithm for the shortest path problem.