Simple and local independent set approximation

Ravi B. Boppana; Magnús M. Halldórsson; Dror Rawitz

doi:10.1007/978-3-030-01325-7_12

Simple and local independent set approximation

Ravi B. Boppana
, Magnús M. Halldórsson
, Dror Rawitz

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

4 Scopus citations

Abstract

We bound the performance guarantees that follow from Turán-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as well as a streaming and preemptive online algorithm. We show it gives a tight (Δ + 1)/2-approximation in unweighted graphs of maximum degree Δ, which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a (Δ + 1)-approximation, but a simple modification results in an asymptotic expected 0.529(Δ + 1)-approximation. This compares with a recent, more complex Δ-approximation [6], which holds determin-istically.

Original language	English
Title of host publication	25th International Colloquium, SIROCCO 2018, Revised Selected Papers
Editors	Zvi Lotker, Boaz Patt-Shamir
Publisher	Springer Verlag
Pages	88-101
Number of pages	14
ISBN (Print)	9783030013240
DOIs	https://doi.org/10.1007/978-3-030-01325-7_12
State	Published - 2018
Event	25th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2018 - Ma’ale HaHamisha, Israel Duration: 18 Jun 2018 → 21 Jun 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11085
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2018
Country/Territory	Israel
City	Ma’ale HaHamisha
Period	18/06/18 → 21/06/18

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2018.

Funding

M. M. Halldórsson—Supported by grants nos. 152679-05 and 174484-05 from the Icelandic Research Fund. D. Rawitz—Supported by the Israel Science Foundation (grant no. 497/14).

Funders	Funder number
Icelandic Research Fund
Israel Science Foundation	497/14

Access to Document

10.1007/978-3-030-01325-7_12

Cite this

Boppana, R. B., Halldórsson, M. M., & Rawitz, D. (2018). Simple and local independent set approximation. In Z. Lotker, & B. Patt-Shamir (Eds.), 25th International Colloquium, SIROCCO 2018, Revised Selected Papers (pp. 88-101). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11085). Springer Verlag. https://doi.org/10.1007/978-3-030-01325-7_12

Boppana, Ravi B. ; Halldórsson, Magnús M. ; Rawitz, Dror. / Simple and local independent set approximation. 25th International Colloquium, SIROCCO 2018, Revised Selected Papers. editor / Zvi Lotker ; Boaz Patt-Shamir. Springer Verlag, 2018. pp. 88-101 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Simple and local independent set approximation",

abstract = "We bound the performance guarantees that follow from Tur{\'a}n-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as well as a streaming and preemptive online algorithm. We show it gives a tight (Δ + 1)/2-approximation in unweighted graphs of maximum degree Δ, which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a (Δ + 1)-approximation, but a simple modification results in an asymptotic expected 0.529(Δ + 1)-approximation. This compares with a recent, more complex Δ-approximation [6], which holds determin-istically.",

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Boppana, RB, Halldórsson, MM & Rawitz, D 2018, Simple and local independent set approximation. in Z Lotker & B Patt-Shamir (eds), 25th International Colloquium, SIROCCO 2018, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11085, Springer Verlag, pp. 88-101, 25th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2018, Ma’ale HaHamisha, Israel, 18/06/18. https://doi.org/10.1007/978-3-030-01325-7_12

Simple and local independent set approximation. / Boppana, Ravi B.; Halldórsson, Magnús M.; Rawitz, Dror.
25th International Colloquium, SIROCCO 2018, Revised Selected Papers. ed. / Zvi Lotker; Boaz Patt-Shamir. Springer Verlag, 2018. p. 88-101 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11085).

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

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AB - We bound the performance guarantees that follow from Turán-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as well as a streaming and preemptive online algorithm. We show it gives a tight (Δ + 1)/2-approximation in unweighted graphs of maximum degree Δ, which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a (Δ + 1)-approximation, but a simple modification results in an asymptotic expected 0.529(Δ + 1)-approximation. This compares with a recent, more complex Δ-approximation [6], which holds determin-istically.

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Boppana RB, Halldórsson MM, Rawitz D. Simple and local independent set approximation. In Lotker Z, Patt-Shamir B, editors, 25th International Colloquium, SIROCCO 2018, Revised Selected Papers. Springer Verlag. 2018. p. 88-101. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-01325-7_12

Simple and local independent set approximation

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