Differential approximation for some routing problems

Bazgan, Cristina; Hassin, Refael; Monnot, Jérôme

Bazgan, Cristina; Hassin, Refael; Monnot, Jérôme (2003), Differential approximation for some routing problems, in Silvestri, Riccardo, Algorithms and Complexity 5th Italian Conference, CIAC 2003, Rome, Italy, May 28-30, 2003, Proceedings, Springer : Berlin Heidelberg, p. 277-288. 10.1007/3-540-44849-7_31

Type

Communication / Conférence

Date

2003

Conference country

ITALY

Book title

Algorithms and Complexity 5th Italian Conference, CIAC 2003, Rome, Italy, May 28-30, 2003, Proceedings

Book author

Silvestri, Riccardo

Publisher

Springer

Published in

Berlin Heidelberg

ISBN

978-3-540-40176-6

Pages

277-288

Abstract (EN)

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: $ \frac{1} {2} $21 for Metric 3VRP, $ \frac{3} {5} $53 for Metric 4VRP, $ \frac{2} {3} $32 for Metric kVRP with k ≥ 5, $ \frac{1} {2} $21 for the nonmetric case for any k ≥ 3, and 1/3 for Constrained VRP. We prove also that Min-Sum EkTSP is $ \frac{2} {3} $32 differential approximable and has no differential approximation scheme, unless P = NP.

Subjects / Keywords

approximation algorithm; differential ratio; VRP; TSP