On the distance constrained vehicle routing problem
Operations Research
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
Approximation algorithms for min-max tree partition
Journal of Algorithms
Transformation of Multisalesman Problem to the Standard Traveling Salesman Problem
Journal of the ACM (JACM)
Approximation Algorithms for Some Postman Problems
Journal of the ACM (JACM)
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximation results for the weighted P4 partition problem
Journal of Discrete Algorithms
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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.