Preliminary Results on Constraint Programming and Branch & Bound Algorithms for the Cyclic Bandwidth Sum Problem

Abstract

The cyclic bandwidth sum problem (CBSP) consists in embedding a host graph into a cycle graph while minimizing the sum of cyclic distances between guest adjacent vertices embedded in the host. While the problem has been addressed by heuristic and metaheuristic methods, to the best of our knowledge, this is the first effort to apply exact methods. This work presents preliminary results on the use of constraint programming (CP) and a branch & bound (B &B) algorithm to solve the cyclic bandwidth sum problem in small graphs from commonly employed topologies. We created a CP model of the CBSP and devised two further refined versions by adding new constraints based in problem-specific knowledge. For our proposed B &B algorithm, we designed a custom criterion for search priority employing estimations of potential cost. The results provided an assessment of the pros and cons of both methodologies, with the CP approach offering a more reliable alternative in terms of solved instances, execution time, and implementation effort.