A category theoretic approach to search algorithms: Towards a unified implementation for branch-and-bound and backtracking

Abstract

Branch-and-bound and backtracking are widely used for search and optimization problems, but their implementations vary from problem to problem. In this paper we propose a unified approach of program derivation and generation for the two classes of algorithms. We first define a generalized specification for the search strategies, and then derive the algorithms, abstract programs and generic programs by incremental refinements on PAR platform, and finally generate efficient programs for concrete problem-solving via colimit computations. Our approach achieves a high level of abstraction and mechanization without losing performance.