Exact and Approximation Algorithms for the Multi-Depot Capacitated Arc Routing Problems

In this work, we investigate a generalization of the classical capacitated arc routing problem, called the Multi-depot Capacitated Arc Routing Problem (MCARP). We give exact and approximation algorithms for different variants of the MCARP. First, we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination version. Second, for the multi-depot rural postman problem, i.e., a special case of the MCARP where the vehicles have infinite capacity, we develop a $\mathrm{(}\mathrm{2}\mathrm{-}\frac{\mathrm{1}}{\mathrm{2}\mathsf{}k\mathrm{+}\mathrm{1}}\mathrm{)}$-approximation algorithm ( $k$ denotes the number of depots). Third, we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line. Lastly, we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness.