Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility

Akihiro Monde; Yukiko Yamauchi; Shuji Kijima; Masafumi Yamashita

doi:10.1007/978-3-319-69084-1_12

Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility

Akihiro Monde, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

Mathematical Informatics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper poses a question about a simple localization problem, which is arisen from self-stabilizing location problems by oblivious mobile autonomous robots with limited visibility. The question is if an oblivious mobile robot on a line-segment can localize the middle point of the line-segment in finite steps observing the direction (i.e., Left or Right) and distance to the nearest end point. This problem is also akin to (a continuous version of) binary search, and could be closely related to computable real functions. Contrary to appearances, it is far from trivial if this simple problem is solvable or not, and unsettled yet. This paper is concerned with three variants of the original problem, minimally relaxing, and presents self-stabilizing algorithms for them. We also show an easy impossibility theorem for bilaterally symmetric algorithms.

Original language	English
Title of host publication	Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Proceedings
Editors	Philippas Tsigas, Paul Spirakis
Publisher	Springer Verlag
Pages	172-186
Number of pages	15
ISBN (Print)	9783319690834
DOIs	https://doi.org/10.1007/978-3-319-69084-1_12
Publication status	Published - Jan 1 2017
Event	19th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2017 - Boston, United States Duration: Nov 5 2017 → Nov 8 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10616 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	19th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2017
Country	United States
City	Boston
Period	11/5/17 → 11/8/17

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-69084-1_12

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Cite this

Monde, A., Yamauchi, Y., Kijima, S., & Yamashita, M. (2017). Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility. In P. Tsigas, & P. Spirakis (Eds.), Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Proceedings (pp. 172-186). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10616 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-69084-1_12

Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility. / Monde, Akihiro; Yamauchi, Yukiko ; Kijima, Shuji; Yamashita, Masafumi.

Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Proceedings. ed. / Philippas Tsigas; Paul Spirakis. Springer Verlag, 2017. p. 172-186 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10616 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Monde, A, Yamauchi, Y , Kijima, S & Yamashita, M 2017, Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility. in P Tsigas & P Spirakis (eds), Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10616 LNCS, Springer Verlag, pp. 172-186, 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2017, Boston, United States, 11/5/17. https://doi.org/10.1007/978-3-319-69084-1_12

Monde A, Yamauchi Y , Kijima S, Yamashita M. Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility. In Tsigas P, Spirakis P, editors, Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Proceedings. Springer Verlag. 2017. p. 172-186. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-69084-1_12

Monde, Akihiro ; Yamauchi, Yukiko ; Kijima, Shuji ; Yamashita, Masafumi. / Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility. Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Proceedings. editor / Philippas Tsigas ; Paul Spirakis. Springer Verlag, 2017. pp. 172-186 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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