Fault-Tolerant Distance Labeling for Planar Graphs

Aviv Bar-Natan; Panagiotis Charalampopoulos; Paweł Gawrychowski; Shay Mozes; Oren Weimann

doi:https://doi.org/10.1007/978-3-030-79527-6_18

Fault-Tolerant Distance Labeling for Planar Graphs

Aviv Bar-Natan, Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, Oren Weimann

Department of Computer Science

University of Haifa

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

Abstract

In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph G such that from the labels of any three vertices u, v, f we can infer the u-to-v distance in the graph G\ { f}. We show that any directed weighted planar graph (and in fact any graph in a graph family with O(n) -size separators, such as minor-free graphs) admits fault-tolerant distance labels of size O(n^{2 / 3}). We extend these labels in a way that allows us to also count the number of shortest paths, and provide additional upper and lower bounds for labels and oracles for counting shortest paths.

Original language	American English
Title of host publication	Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings
Editors	Tomasz Jurdziński, Stefan Schmid
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	315-333
Number of pages	19
ISBN (Print)	9783030795269
DOIs	https://doi.org/10.1007/978-3-030-79527-6_18
State	Published - 2021
Event	28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021 - Virtual, Online Duration: 28 Jun 2021 → 1 Jul 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12810 LNCS

Conference

Conference	28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021
City	Virtual, Online
Period	28/06/21 → 1/07/21

Keywords

Counting shortest paths
Fault-tolerant distance labels
Forbidden-set distance labels
Planar graphs

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

https://doi.org/10.1007/978-3-030-79527-6_18

Cite this

Bar-Natan, A., Charalampopoulos, P., Gawrychowski, P., Mozes, S., & Weimann, O. (2021). Fault-Tolerant Distance Labeling for Planar Graphs. In T. Jurdziński, & S. Schmid (Eds.), Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings (pp. 315-333). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12810 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-79527-6_18

Bar-Natan, Aviv ; Charalampopoulos, Panagiotis ; Gawrychowski, Paweł et al. / Fault-Tolerant Distance Labeling for Planar Graphs. Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings. editor / Tomasz Jurdziński ; Stefan Schmid. Springer Science and Business Media Deutschland GmbH, 2021. pp. 315-333 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph G such that from the labels of any three vertices u, v, f we can infer the u-to-v distance in the graph G\ { f}. We show that any directed weighted planar graph (and in fact any graph in a graph family with O(n) -size separators, such as minor-free graphs) admits fault-tolerant distance labels of size O(n2 / 3). We extend these labels in a way that allows us to also count the number of shortest paths, and provide additional upper and lower bounds for labels and oracles for counting shortest paths.",

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author = "Aviv Bar-Natan and Panagiotis Charalampopoulos and Pawe{\l} Gawrychowski and Shay Mozes and Oren Weimann",

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Bar-Natan, A, Charalampopoulos, P, Gawrychowski, P, Mozes, S & Weimann, O 2021, Fault-Tolerant Distance Labeling for Planar Graphs. in T Jurdziński & S Schmid (eds), Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12810 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 315-333, 28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021, Virtual, Online, 28/06/21. https://doi.org/10.1007/978-3-030-79527-6_18

Fault-Tolerant Distance Labeling for Planar Graphs. / Bar-Natan, Aviv; Charalampopoulos, Panagiotis; Gawrychowski, Paweł et al.
Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings. ed. / Tomasz Jurdziński; Stefan Schmid. Springer Science and Business Media Deutschland GmbH, 2021. p. 315-333 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12810 LNCS).

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

TY - GEN

T1 - Fault-Tolerant Distance Labeling for Planar Graphs

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AU - Gawrychowski, Paweł

AU - Mozes, Shay

AU - Weimann, Oren

PY - 2021

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AB - In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph G such that from the labels of any three vertices u, v, f we can infer the u-to-v distance in the graph G\ { f}. We show that any directed weighted planar graph (and in fact any graph in a graph family with O(n) -size separators, such as minor-free graphs) admits fault-tolerant distance labels of size O(n2 / 3). We extend these labels in a way that allows us to also count the number of shortest paths, and provide additional upper and lower bounds for labels and oracles for counting shortest paths.

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KW - Forbidden-set distance labels

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DO - https://doi.org/10.1007/978-3-030-79527-6_18

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Y2 - 28 June 2021 through 1 July 2021

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Bar-Natan A, Charalampopoulos P, Gawrychowski P, Mozes S, Weimann O. Fault-Tolerant Distance Labeling for Planar Graphs. In Jurdziński T, Schmid S, editors, Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 315-333. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: https://doi.org/10.1007/978-3-030-79527-6_18

Fault-Tolerant Distance Labeling for Planar Graphs

Abstract

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Conference

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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