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: [email protected] (E.M. Arkin), [email protected] (R. Hassin), [email protected] (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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:33646440993
SN - 0196-6774
VL - 59
SP - 1
EP - 18
JO - Journal of Algorithms
JF - Journal of Algorithms
IS - 1
ER -