Red-Blue-Partitioned MST, TSP, and Matching

Abstract

Arkin et al. [2] recently introduced partitioned pairs network optimization problems: given a metricweighted graph on n pairs of nodes, the task is to color one node from each pair red and the other blue, and then to compute two separate network structures or disjoint (node-covering) subgraphs of a specified sort, one on the graph induced by the red nodes and the other on the blue nodes. Three structures have been investigated by [2]-spanning trees, traveling salesperson tours, and perfect matchings-and the three objectives to optimize for when computing such pairs of structures: min-sum, min-max, and bottleneck. We provide improved approximation guarantees and/or strengthened hardness results for these nine NP-hard problem settings.