On matchings, T-joins and arc routing problems

Boyacı, Burak and Dang, Thu and Letchford, Adam (2022) On matchings, T-joins and arc routing problems. Networks, 79 (1). pp. 20-31. ISSN 0028-3045

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Abstract

Matchings and T-joins are fundamental and much-studied concepts in graph theory and combinatorial optimisation. 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.