Approximation Algorithms for Mixed, Windy, and Capacitated Arc Routing Problems

We show that any α(n)-approximation algorithm for the n-vertex metric asymmetric Traveling Salesperson problem yields O(α(C))-approximation algorithms for various mixed, windy, and capacitated arc routing problems. Herein, C is the number of weakly-connected components in the subgraph induced by the positive-demand arcs, a number that can be expected to be small in applications. In conjunction with known results, we derive constant-factor approximations if C ∈ O(logn) and O ( logC/log logC ) -approximations in general. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.1.6 Optimization, G.2.1 Combinatorics, G.2.2 Graph Theory, I.2.8 Problem Solving, Control Methods, and Search