On the distance constrained vehicle routing problem
Operations Research
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Theoretical Computer Science
Combinatorial optimization
Transformation of Multisalesman Problem to the Standard Traveling Salesman Problem
Journal of the ACM (JACM)
P-Complete Approximation Problems
Journal of the ACM (JACM)
Journal of Algorithms
Differential approximation results for the traveling salesman and related problems
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the completeness of a generalized matching problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On the complexity of the k-customer vehicle routing problem
Operations Research Letters
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We study vehicle routing problems with constraints on the distance traveled by each vehicle or on the number of vehicles. The objective is to minimize the total distance traveled by vehicles. We design constant differential approximation algorithms for some of these problems. In particular we obtain differential bounds: 1/2 for Metric 3VRP, 3/5 for Metric 4VRP, 2/3 for Metric kVRP with k ≥ 5, 1/2 for the nonmetric case for any k ≥ 3, and 1/3 for Constrained VRP. We prove also that Min-Sum EkTSP is 2/3 differential approximable and has no differential approximation scheme, unless P = NP.