Article

Approximation algorithms for euclidean group TSP

Authors:

Khaled Elbassioni,

Aleksei V. Fishkin,

Nabil H. Mustafa,

René SittersAuthors Info & Claims

ICALP'05: Proceedings of the 32nd international conference on Automata, Languages and Programming

Pages 1115 - 1126

https://doi.org/10.1007/11523468_90

Published: 11 July 2005 Publication History

Abstract

In the Euclidean group Traveling Salesman Problem (TSP), we are given a set of points P in the plane and a set of m connected regions, each containing at least one point of P. We want to find a tour of minimum length that visits at least one point in each region. This unifies the TSP with Neighborhoods and the Group Steiner Tree problem. We give a (9.1α+1)-approximation algorithm for the case when the regions are disjoint α-fat objects with possibly varying size. This considerably improves the best results known, in this case, for both the group Steiner tree problem and the TSP with Neighborhoods problem. We also give the first O(1)-approximation algorithm for the problem with intersecting regions.

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Chan TJiang S(2018)Reducing Curse of DimensionalityACM Transactions on Algorithms10.1145/315823214:1(1-18)Online publication date: 3-Jan-2018
https://dl.acm.org/doi/10.1145/3158232
Chan TJiang S(2016)Reducing curse of dimensionalityProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884489(754-765)Online publication date: 10-Jan-2016
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Approximation algorithms for euclidean group TSP
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
  2. Mathematical analysis
    1. Functional analysis
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

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Published In

cover image Guide Proceedings

ICALP'05: Proceedings of the 32nd international conference on Automata, Languages and Programming

July 2005

1476 pages

ISBN:3540275800

Editors:
Luís Caires
CITI / Departamento de Informática, Universidade Nova de Lisboa, Portugal
,
Giuseppe F. Italiano
Dipartimento di Informatica, Sistemi e Produzione, Università di Roma "Tor Vergata", via del Politecnico 1, Roma, Italy
,
Luís Monteiro
Departamento de Informatica, Universidade Nova de Lisboa, via del Politecnico 1, Caparica, Portugal
,
Catuscia Palamidessi
Departamento de Informatica, Ecole Polytechnique, Rue de Saclay, Palaiseau Cedex, France
,
Moti Yung
Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, New York, France

Sponsors

Fundacao para a Ciencia e Tecnologia
FCT: Foundation for Science and Technology
Centro de Lógica e Computação/IST/UTL: Centro de Lógica e Computação/IST/UTL

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 11 July 2005

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Cited By

Anthony BChristman AChung CYuen D(2021)Serving Rides of Equal Importance for Time-Limited Dial-a-RideMathematical Optimization Theory and Operations Research10.1007/978-3-030-77876-7_3(35-50)Online publication date: 5-Jul-2021
https://dl.acm.org/doi/10.1007/978-3-030-77876-7_3
Chan TJiang S(2018)Reducing Curse of DimensionalityACM Transactions on Algorithms10.1145/315823214:1(1-18)Online publication date: 3-Jan-2018
https://dl.acm.org/doi/10.1145/3158232
Chan TJiang S(2016)Reducing curse of dimensionalityProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884489(754-765)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884489
Dumitrescu ATóth C(2016)The Traveling Salesman Problem for Lines, Balls, and PlanesACM Transactions on Algorithms10.1145/285041812:3(1-29)Online publication date: 25-Apr-2016
https://dl.acm.org/doi/10.1145/2850418
Bhattacharya BăźUstić ARafiey ARafiey ASokol V(2015)Approximation Algorithms for Generalized MST and TSP in Grid ClustersProceedings of the 9th International Conference on Combinatorial Optimization and Applications - Volume 948610.1007/978-3-319-26626-8_9(110-125)Online publication date: 18-Dec-2015
https://dl.acm.org/doi/10.1007/978-3-319-26626-8_9
Dumitrescu ATóth CKhanna S(2013)The traveling salesman problem for lines, balls and planesProceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms10.5555/2627817.2627876(828-843)Online publication date: 6-Jan-2013
https://dl.acm.org/doi/10.5555/2627817.2627876
Guimaraes Macharet DAlves Neto AFiuza da Camara Neto VMontenegro Campos MMoore J(2012)An evolutionary approach for the dubins' traveling salesman problem with neighborhoodsProceedings of the 14th annual conference on Genetic and evolutionary computation10.1145/2330163.2330218(377-384)Online publication date: 7-Jul-2012
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Chen DMisiolek E(2011)Algorithms for interval structures with applicationsProceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management10.5555/2021911.2021936(196-207)Online publication date: 28-May-2011
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Sugihara RGupta R(2011)Path Planning of Data Mules in Sensor NetworksACM Transactions on Sensor Networks10.1145/1993042.19930438:1(1-27)Online publication date: 1-Aug-2011
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Yuan YPeng Y(2010)RacetrackProceedings of the 9th international conference on Ad-hoc, mobile and wireless networks10.5555/1881991.1882002(135-148)Online publication date: 20-Aug-2010
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