Constant-factor approximations for Capacitated Arc Routing without   triangle inequality
  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 {\alpha} approximation for CARP with triangle inequality yields a factor {\alpha} approximation for the general CARP. 
Ren\'e van Bevern, Sepp Hartung, Andr\'e Nichterlein, Manuel Sorge
cs.DS cs.DM math.CO