Open AccessDifferential Approximation for Some Routing Problems
Author(s) -
Cristina Bazgan,
Refael Hassin,
Jérôme Monnot
Publication year - 2003
Publication title -
lecture notes in computer science
Language(s) - English
Resource type - Book series
SCImago Journal Rank - 0.249
H-Index - 400
eISSN - 1611-3349
pISSN - 0302-9743
DOI - 10.1007/3-540-44849-7_31
Subject(s) - metric (unit) , routing (electronic design automation) , differential (mechanical device) , vehicle routing problem , combinatorics , metric space , constant (computer programming) , mathematics , scheme (mathematics) , discrete mathematics , computer science , algorithm , physics , mathematical analysis , engineering , operations management , programming language , computer network , thermodynamics
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom