Randomized Rounding for Routing and Covering Problems: Experiments and Improvements

We investigate how the recently developed different approaches to generate randomized roundings satisfying disjoint cardinality constraints behave when used in two classical algorithmic problems, namely low-congestion routing in networks and max-coverage problems in hypergraphs. Based on our experiments, we also propose and investigate the following new ideas. For the low-congestion routing problems, we suggest to solve a second LP, which yields the same congestion, but aims at producing a solution that is easier to round. For the max-coverage instances, observing that the greedy heuristic also performs very good, we develop hybrid approaches, in the form of a strengthened method of derandomized rounding, and a simple greedy/rounding hybrid using greedy and LP-based rounding elements. Experiments show that these ideas significantly reduce the rounding errors. For an important special case of max-coverage, namely unit disk max-domination, we also develop a PTAS. However, experiments show it less competitive than other approaches, except possibly for extremely high solution qualities.