Approximation algorithms for the set cover formation by oblivious mobile robots

Tomoko Izumi, Sayaka Kamei, Yukiko Yamauchi

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

1 Citation (Scopus)

Abstract

Given n robots and n target points on the plane, the minimum set cover formation (SCF) problem requires the robots to form a set cover by the minimum number of robots. In previous formation problems by mobile robots, such as gathering and pattern formation, the problems consist only of the mobile robots, and there are no points fixed in the environment. In addition, the problems do not require a control of the number of robots constructing the formation. In this paper, we first introduce the formation problem in which robots move so that they achieve a desired deployment with the minimum number of robots for a given set of positions of fixed points.

Since the minimum set cover problem with disks in the centralized settings is NP-hard, our goal is to propose approximation algorithms for the minimum SCF problem. First, we show a minimal SCF algorithm from any initial configuration in the asynchronous system. Moreover, we propose an 8-approximation SCF algorithm in the semi-synchronous system for an initial configuration with a low symmetricity. This approximation algorithm achieves 2(1 + 1/l)2 approximation ratio for an initial configuration with the lowest symmetricity (l ≥ 1).

Original languageEnglish
Title of host publicationPrinciples of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings
EditorsMarcos K. Aguilera, Leonardo Querzoni, Marc Shapiro
PublisherSpringer Verlag
Pages233-247
Number of pages15
ISBN (Electronic)9783319144719
Publication statusPublished - Jan 1 2014
Event18th International Conference on Principles of Distributed Systems, OPODIS 2014 - Cortina d’Ampezzo, Italy
Duration: Dec 16 2014Dec 19 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8878
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other18th International Conference on Principles of Distributed Systems, OPODIS 2014
CountryItaly
CityCortina d’Ampezzo
Period12/16/1412/19/14

Fingerprint

Set Cover
Approximation algorithms
Mobile Robot
Mobile robots
Approximation Algorithms
Robots
Robot
Configuration
Fixed point
Synchronous Systems
Asynchronous Systems
Minimal Set
Approximation
Pattern Formation
Lowest
NP-complete problem
Target

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Izumi, T., Kamei, S., & Yamauchi, Y. (2014). Approximation algorithms for the set cover formation by oblivious mobile robots. In M. K. Aguilera, L. Querzoni, & M. Shapiro (Eds.), Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings (pp. 233-247). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8878). Springer Verlag.

Approximation algorithms for the set cover formation by oblivious mobile robots. / Izumi, Tomoko; Kamei, Sayaka; Yamauchi, Yukiko.

Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings. ed. / Marcos K. Aguilera; Leonardo Querzoni; Marc Shapiro. Springer Verlag, 2014. p. 233-247 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8878).

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

Izumi, T, Kamei, S & Yamauchi, Y 2014, Approximation algorithms for the set cover formation by oblivious mobile robots. in MK Aguilera, L Querzoni & M Shapiro (eds), Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8878, Springer Verlag, pp. 233-247, 18th International Conference on Principles of Distributed Systems, OPODIS 2014, Cortina d’Ampezzo, Italy, 12/16/14.
Izumi T, Kamei S, Yamauchi Y. Approximation algorithms for the set cover formation by oblivious mobile robots. In Aguilera MK, Querzoni L, Shapiro M, editors, Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings. Springer Verlag. 2014. p. 233-247. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Izumi, Tomoko ; Kamei, Sayaka ; Yamauchi, Yukiko. / Approximation algorithms for the set cover formation by oblivious mobile robots. Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings. editor / Marcos K. Aguilera ; Leonardo Querzoni ; Marc Shapiro. Springer Verlag, 2014. pp. 233-247 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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