On matchings, T-joins, and arc routing in road networks

Abstract

Matchings and T-joins are fundamental and much-studied concepts in graph theory and combinatorial optimization. One important application of matchings and T-joins is in the computation of strong lower bounds for arc routing problems (ARPs). An ARP is a special kind of vehicle routing problem, in which the demands are located along edges or arcs, rather than at nodes. We point out that the literature on applying matchings and T-joins to ARPs does not fully exploit the structure of real-life road networks. We propose some ways to exploit this structure. Computational results show significant running time improvements, without deteriorating the quality of the lower bounds.