The very offline k-vehicle routing problem in trees

The vehicle routing problem (VRP) in trees is a restriction of the general vehicle routing problem in which the underlying graph is a tree. In this paper we introduce several NP-complete variants of the problem (e.g., common-source, common-destinations, in-place, flexible-requests, and bring-it-back), and we present five fast approximation algorithms for these variants. We mainly focus on the 2-vehicle routing problems, but we also consider possible generalizations for the k-vehicle routing case. In our analysis, the underlying graphs consist of various types of trees: binary and non-binary weighted and unweighted