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.

Improving a constructive heuristic for the general routing problem

“…Finally, Boyac𝚤 et al [4] pointed out that the Korte-Vygen approach is well-suited to CPP instances on road networks, since road networks have bounded degree. Using the Korte-Vygen approach in conjunction with an open-source matching routine, they were able to solve CPP instances with 50 000 nodes in less than a second on a laptop.…”

“…In road networks, most nodes have degree less than 5. As a result, when applied to a WTJ on a road network, the Korte–Vygen algorithm involves the solution of a matching problem with only $$$ \mid V\mid $$$ nodes and edges (see also [4]).…”