TY - JOUR

T1 - Approximations for minimum and min-max vehicle routing problems

AU - Arkin, Esther M.

AU - Hassin, Refael

AU - Levin, Asaf

N1 - Funding Information:
* Corresponding author. Present address: Department of Statistics, The Hebrew University, Jerusalem 91905, Israel. E-mail addresses: estie@ams.sunysb.edu (E.M. Arkin), hassin@post.tau.ac.il (R. Hassin), levinas@mscc.huji.ac.il (A. Levin). 1 Partially supported by NSF (CCR-0098172).

PY - 2006/4

Y1 - 2006/4

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Edge-routing

KW - Min-max problems

KW - Vehicle routing problem

UR - http://www.scopus.com/inward/record.url?scp=33646440993&partnerID=8YFLogxK

U2 - 10.1016/j.jalgor.2005.01.007

DO - 10.1016/j.jalgor.2005.01.007

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AN - SCOPUS:33646440993

SN - 0196-6774

VL - 59

SP - 1

EP - 18

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 1

ER -