Constant-factor approximations for Capacitated Arc Routing without triangle inequality

René van Bevern, Sepp Hartung, André Nichterlein, Manuel Sorge

Abstract: Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation algorithms were proposed for CARP with triangle inequality, while CARP was claimed to be NP-hard to approximate within any constant factor in general. Correcting this claim, we show that any factor  α<math><mi is="true">α</mi></math> approximation for CARP with triangle inequality yields a factor  α<math><mi is="true">α</mi></math> approximation for the general CARP.