Approximation and Polynomial Algorithms for Multi-depot Capacitated Arc Routing Problems

Abstract

AbstractWe study the multi-depot capacitated arc routing problem (MCARP), which generalizes the classical arc routing problem to the more realistic situation with multiple depots. We propose approximation and polynomial algorithms for different variants of the MCARP. First, we present the first constant-factor approximation algorithms for the MCARP and the nonfixed destination variant. Second, for a restricted case of the MCARP with infinite vehicle capacity, called the multi-depot rural postman problem, we devise a \((2-\frac{1}{2k+1})\)-approximation algorithm with k indicating the number of depots. Lastly, we show that the equal-demand MCARP defined on a line graph is polynomially solvable and develop a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line.KeywordsApproximation algorithmMulti-depotVehicle routing problemArc routing problemRural postman problem