Approximating the generalized minimum Manhattan network problem

Aparna Das, Krzysztof Fleszar, Stephen G Kobourov, Joachim Spoerhase, Sankar Veeramoni, Alexander Wolff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in ℝ2. The goal is to find a minimum-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line segments whose total length equals the pair's Manhattan distance. This problem is a natural generalization of the extensively studied minimum Manhattan network problem (MMN) in which R consists of all possible pairs of terminals. Another important special case is the well-known rectilinear Steiner arborescence problem (RSA). As a generalization of these problems, GMMN is NP-hard. No approximation algorithms are known for general GMMN. We obtain an O(logn)-approximation algorithm for GMMN. Our solution is based on a stabbing technique, a novel way of attacking Manhattan network problems. Some parts of our algorithm generalize to higher dimensions, yielding a simple O(log d+1 n)-approximation algorithm for the problem in arbitrary fixed dimension d. As a corollary, we obtain an exponential improvement upon the previously best O(n ε )-ratio for MMN in d dimensions [ESA'11]. En route, we show that an existing O(logn)-approximation algorithm for 2D-RSA generalizes to higher dimensions.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages722-732
Number of pages11
Volume8283 LNCS
DOIs
StatePublished - 2013
Event24th International Symposium on Algorithms and Computation, ISAAC 2013 - Hong Kong, China
Duration: Dec 16 2013Dec 18 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8283 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other24th International Symposium on Algorithms and Computation, ISAAC 2013
CountryChina
CityHong Kong
Period12/16/1312/18/13

Fingerprint

Approximation algorithms
Approximation Algorithms
Steiner's problem
Computational complexity
Higher Dimensions
Path
Generalise
Line segment
Corollary
NP-complete problem

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Das, A., Fleszar, K., Kobourov, S. G., Spoerhase, J., Veeramoni, S., & Wolff, A. (2013). Approximating the generalized minimum Manhattan network problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8283 LNCS, pp. 722-732). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS). https://doi.org/10.1007/978-3-642-45030-3_67

Approximating the generalized minimum Manhattan network problem. / Das, Aparna; Fleszar, Krzysztof; Kobourov, Stephen G; Spoerhase, Joachim; Veeramoni, Sankar; Wolff, Alexander.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8283 LNCS 2013. p. 722-732 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Das, A, Fleszar, K, Kobourov, SG, Spoerhase, J, Veeramoni, S & Wolff, A 2013, Approximating the generalized minimum Manhattan network problem. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8283 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8283 LNCS, pp. 722-732, 24th International Symposium on Algorithms and Computation, ISAAC 2013, Hong Kong, China, 12/16/13. https://doi.org/10.1007/978-3-642-45030-3_67
Das A, Fleszar K, Kobourov SG, Spoerhase J, Veeramoni S, Wolff A. Approximating the generalized minimum Manhattan network problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8283 LNCS. 2013. p. 722-732. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-45030-3_67
Das, Aparna ; Fleszar, Krzysztof ; Kobourov, Stephen G ; Spoerhase, Joachim ; Veeramoni, Sankar ; Wolff, Alexander. / Approximating the generalized minimum Manhattan network problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8283 LNCS 2013. pp. 722-732 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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