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The Multidepot Capacitated Vehicle Routing Problem (MCVRP) is a well-knownvariant of the classic Capacitated Vehicle Routing Problem (CVRP), where weneed to route capacitated vehicles located in multiple depots to servecustomers' demand such that each vehicle must return to the depot it starts,and the total traveling distance is minimized. There are three variants ofMCVRP according to the property of the demand: unit-demand, splittable andunsplittable. We study approximation algorithms for $k$-MCVRP in metric graphs,where $k$ is the capacity of each vehicle. The best-known approximation ratiosfor the three versions are $4-\Theta(1/k)$, $4-\Theta(1/k)$, and $4$,respectively. We give a $(4-1/1500)$-approximation algorithm for unit-demandand splittable $k$-MCVRP, and a $(4-1/50000)$-approximation algorithm forunsplittable $k$-MCVRP. When $k$ is a fixed integer, we give a$(3+\ln2-\max\{\Theta(1/\sqrt{k}),1/9000\})$-approximation algorithm for thesplittable and unit-demand cases, and a$(3+\ln2-\Theta(1/\sqrt{k}))$-approximation algorithm for the unsplittablecase.

Multidepot Capacitated Vehicle Routing with Improved Approximation Guarantees