Polynomial lower bound for distributed graph coloring in a weak LOCAL model

Dan Hefetz; Fabian Kuhn; Yannic Maus; Angelika Steger

doi:10.1007/978-3-662-53426-7_8

Polynomial lower bound for distributed graph coloring in a weak LOCAL model

Dan Hefetz, Fabian Kuhn, Yannic Maus, Angelika Steger

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

17 Scopus citations

Abstract

We show an Ω(formula presented) lower bound on the runtime of any deterministic distributed O(Δ^1+η)-graph coloring algorithm in a weak variant of the LOCAL model. In particular, given a network graph G = (V,E), in the weak LOCAL model nodes communicate in synchronous rounds and they can use unbounded local computation. The nodes have no identifiers, but instead, the computation starts with an initial valid vertex coloring. A node can broadcast a single message of unbounded size to its neighbors and receives the set of messages sent to it by its neighbors. The proof uses neighborhood graphs and improves their understanding in general such that it might help towards finding a lower (runtime) bound for distributed graph coloring in the standard LOCAL model.

Original language	English
Title of host publication	Distributed Computing - 30th International Symposium, DISC 2016, Proceedings
Editors	Cyril Gavoille, David Ilcinkas
Pages	99-113
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-662-53426-7_8
State	Published - 2016
Externally published	Yes
Event	30th International Symposium on Distributed Computing, DISC 2016 - Paris, France Duration: 27 Sep 2016 → 29 Sep 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9888 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	30th International Symposium on Distributed Computing, DISC 2016
Country/Territory	France
City	Paris
Period	27/09/16 → 29/09/16

Keywords

Color reduction
Distributed graph coloring
Distributed symmetry breaking
LOCAL model
Lower bound
Neighborhood graphs

Access to Document

10.1007/978-3-662-53426-7_8

Cite this

Hefetz, D., Kuhn, F., Maus, Y., & Steger, A. (2016). Polynomial lower bound for distributed graph coloring in a weak LOCAL model. In C. Gavoille, & D. Ilcinkas (Eds.), Distributed Computing - 30th International Symposium, DISC 2016, Proceedings (pp. 99-113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9888 LNCS). https://doi.org/10.1007/978-3-662-53426-7_8

Hefetz, Dan ; Kuhn, Fabian ; Maus, Yannic et al. / Polynomial lower bound for distributed graph coloring in a weak LOCAL model. Distributed Computing - 30th International Symposium, DISC 2016, Proceedings. editor / Cyril Gavoille ; David Ilcinkas. 2016. pp. 99-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We show an Ω(formula presented) lower bound on the runtime of any deterministic distributed O(Δ1+η)-graph coloring algorithm in a weak variant of the LOCAL model. In particular, given a network graph G = (V,E), in the weak LOCAL model nodes communicate in synchronous rounds and they can use unbounded local computation. The nodes have no identifiers, but instead, the computation starts with an initial valid vertex coloring. A node can broadcast a single message of unbounded size to its neighbors and receives the set of messages sent to it by its neighbors. The proof uses neighborhood graphs and improves their understanding in general such that it might help towards finding a lower (runtime) bound for distributed graph coloring in the standard LOCAL model.",

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Hefetz, D, Kuhn, F, Maus, Y & Steger, A 2016, Polynomial lower bound for distributed graph coloring in a weak LOCAL model. in C Gavoille & D Ilcinkas (eds), Distributed Computing - 30th International Symposium, DISC 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9888 LNCS, pp. 99-113, 30th International Symposium on Distributed Computing, DISC 2016, Paris, France, 27/09/16. https://doi.org/10.1007/978-3-662-53426-7_8

Polynomial lower bound for distributed graph coloring in a weak LOCAL model. / Hefetz, Dan; Kuhn, Fabian; Maus, Yannic et al.
Distributed Computing - 30th International Symposium, DISC 2016, Proceedings. ed. / Cyril Gavoille; David Ilcinkas. 2016. p. 99-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9888 LNCS).

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

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Hefetz D, Kuhn F, Maus Y, Steger A. Polynomial lower bound for distributed graph coloring in a weak LOCAL model. In Gavoille C, Ilcinkas D, editors, Distributed Computing - 30th International Symposium, DISC 2016, Proceedings. 2016. p. 99-113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-53426-7_8

Polynomial lower bound for distributed graph coloring in a weak LOCAL model

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