Approximations for minimum and min-max vehicle routing problems

Esther M. Arkin, Refael Hassin, Asaf Levin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider a variety of vehicle routing problems. The input to a problem consists of a graph G = ( N, E ) and edge lengths l ( e ), e ∈ E. Customers located at the vertices have to be visited by a set of vehicles. Two important parameters are k the number of vehicles, and λ the longest distance traveled by a vehicle. We consider two types of problems. (1) Given a bound λ on the length of each path, find a minimum sized collection of paths that cover all the vertices of the graph, or all the edges from a given subset of edges of the input graph. We also consider a variation where it is desired to cover N by a minimum number of stars of length bounded by λ. (2) Given a number k find a collection of k paths that cover either the vertex set of the graph or a given subset of edges. The goal here is to minimize λ, the maximum travel distance. For all these problems we provide constant ratio approximation algorithms and prove their NP-hardness.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Algorithms
Issue number1
StatePublished - Apr 2006


  • Approximation algorithms
  • Edge-routing
  • Min-max problems
  • Vehicle routing problem


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