A faster branch-and-bound algorithm for the test-cover problem based on set-covering techniques

Abstract

The test-cover problem asks for the minimal number of tests needed to uniquely identify a disease, infection, etc. A collection of branch-and-bound algorithms was proposed by De Bontridder et al. [2002]. Based on their work, we introduce several improvements that are compatible with all techniques described in De Bontridder et al. [2002] and the more general setting of weighted test-cover problems. We present a faster data structure, cost-based variable fixing, and adapt well-known set-covering techniques, including Lagrangian relaxation and upper-bound heuristics. The resulting algorithm solves benchmark instances up to 10 times faster than the former approach and up to 100 times faster than a general MIP solver.