Simple and local independent set approximation

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

doi:10.1016/j.tcs.2020.09.018

Simple and local independent set approximation

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

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Massachusetts Institute of Technology
Reykjavík University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study the worst-case behavior of Turán-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, we revisit a randomized approach of Boppana that forms a simple 1-round distributed algorithm, as well as a streaming algorithm and a preemptive online algorithm. We show that 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.

Original language	English
Pages (from-to)	27-37
Number of pages	11
Journal	Theoretical Computer Science
Volume	846
DOIs	https://doi.org/10.1016/j.tcs.2020.09.018
State	Published - 18 Dec 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Funding

Magnús M. Halldórsson was partially supported by the Icelandic Research Fund (grants nos. 152679-05 and 174484-05 ). Dror Rawitz was partially supported by the Israel Science Foundation (grant no. 497/14 ). Magn?s M. Halld?rsson was partially supported by the Icelandic Research Fund (grants nos. 152679-05 and 174484-05). Dror Rawitz was partially supported by the Israel Science Foundation (grant no. 497/14).

Funders	Funder number
Icelandic Research Fund
Icelandic Centre for Research	174484-05, 152679-05
Israel Science Foundation	497/14

Keywords

Approximation algorithm
Distributed algorithm
Independent set
Turán bound

Access to Document

10.1016/j.tcs.2020.09.018

Cite this

@article{c86a7504f756483b91eac58fa2379ba4,

title = "Simple and local independent set approximation",

abstract = "We study the worst-case behavior of Tur{\'a}n-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, we revisit a randomized approach of Boppana that forms a simple 1-round distributed algorithm, as well as a streaming algorithm and a preemptive online algorithm. We show that 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.",

keywords = "Approximation algorithm, Distributed algorithm, Independent set, Tur{\'a}n bound",

author = "Boppana, \{Ravi B.\} and Halld{\'o}rsson, \{Magn{\'u}s M.\} and Dror Rawitz",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = dec,

day = "18",

doi = "10.1016/j.tcs.2020.09.018",

language = "אנגלית",

volume = "846",

pages = "27--37",

journal = "Theoretical Computer Science",

issn = "0304-3975",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Simple and local independent set approximation

AU - Boppana, Ravi B.

AU - Halldórsson, Magnús M.

AU - Rawitz, Dror

PY - 2020/12/18

Y1 - 2020/12/18

N2 - We study the worst-case behavior of Turán-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, we revisit a randomized approach of Boppana that forms a simple 1-round distributed algorithm, as well as a streaming algorithm and a preemptive online algorithm. We show that 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.

AB - We study the worst-case behavior of Turán-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, we revisit a randomized approach of Boppana that forms a simple 1-round distributed algorithm, as well as a streaming algorithm and a preemptive online algorithm. We show that 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.

KW - Approximation algorithm

KW - Distributed algorithm

KW - Independent set

KW - Turán bound

UR - https://www.scopus.com/pages/publications/85091047541

U2 - 10.1016/j.tcs.2020.09.018

DO - 10.1016/j.tcs.2020.09.018

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85091047541

SN - 0304-3975

VL - 846

SP - 27

EP - 37

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Simple and local independent set approximation

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this