On the distance constrained vehicle routing problem
Operations Research
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Maximizing the number of unused colors in the vertex coloring problem
Information Processing Letters
Theoretical Computer Science
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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)
On the approximability of the traveling salesman problem (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Better approximations for max TSP
Information Processing Letters
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
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the completeness of a generalized matching problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A better differential approximation ratio for symmetric TSP
Theoretical Computer Science
New differential approximation algorithm for k-customer vehicle routing problem
Information Processing 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 either to minimize the total distance traveled by vehicles or to minimize the number of vehicles used. We design constant differential approximation algorithms for kVRP. Note that, using the differential bound for METRIC 3VRP, we obtain the randomized standard ratio 197/99 + ε ∀ε 0. This is an improvement of the best-known bound of 2 given by Haimovich et al. (Vehicle Routing Methods and Studies, Golden, Assad, editors, Elsevier, Amsterdam, 1988). For natural generalizations of this problem, called EDGE COST VRP, VERTEX COST VRP, MIN VEHICLE and kTSP we obtain constant differential approximation algorithms and we show that these problems have no differential approximation scheme, unless P = NP.