Approximation algorithms for solving the constrained arc routing problem in mixed graphs

A parameterized approximation algorithm for the mixed and windy capacitated arc routing problem: Theory and experiments

“…One barrier for generalizing this result to MWCARP is that already approximating MWRPP is challenging (see Section 1.2). Indeed, the only polynomial-time algorithms with guaranteed solution quality for arc routing problems in mixed graphs are for variants to which Observation 1.6 does not apply since all arcs and edges have to be served [15,37]. Our algorithm follows the "route first, cluster second" approach: We first compute an approximate giant tour using Theorem 1.7(ii) and then, analogously to the approximation algorithms for undirected CARP [31,41], split it to obtain Theorem 1.7(iii).…”

“…One barrier for generalizing this result to MWCARP is that already approximating MWRPP is challenging (see Section 1.2). Indeed, the only polynomial-time algorithms with guaranteed solution quality for arc routing problems in mixed graphs are for variants to which Observation 1.6 does not apply since all arcs and edges have to be served [15,37].…”

An updated annotated bibliography on arc routing problems

“…A 3-regular graph is a graph where all nodes share the same degree, it being equal to 3. Moreover, solving [45,124] Including TW constraints [124] Generalized or close-enough [124] CPP solutions on 3-regular (multi)graphs [186] With load-dependent costs -the cost of traversing an edge depends on its length and on the weight of the vehicle's cargo [61] Edge-colored multigraph -each edge has a color, and a tour is called properly colored if no two consecutive edges share the same color [45,68,194] MCPP Min(cost) 100,194] Lower and upper bounds on the number of times each link is traversed [76] WCPP Min(cost) W A R = ∅ E R = E N R = ∅ Costs on links depend on the travel direction [66,68,194] HCPP Min(cost) U A R = ∅ E R = E N R = ∅ Links in a higher hierarchic level need to be serviced before links in lower levels [124] TDCPP Min(cost) D A R = A E R = ∅ N R = ∅ Time-dependent -the time needed to service a link depends on the service start time [187,190] (Continued)…”

“…Ding et al study a generalization of the mixed CPP that introduces lower and upper bounds on the number of times each link is traversed. The goal is to identify a minimum cost tour, beginning and ending at the depot, traversing each link within its previously specified bounds.…”