research-article

Efficient Reductions and a Fast Algorithm of Maximum Weighted Independent Set

Authors:

Bolin DingAuthors Info & Claims

WWW '21: Proceedings of the Web Conference 2021

Pages 3930 - 3940

https://doi.org/10.1145/3442381.3450130

Published: 03 June 2021 Publication History

Abstract

The maximum independent set problem is one of the most fundamental problems in graph algorithms and has been widely studied in social networks. The weighted version of this problem, where each vertex is assigned a nonnegative weight, also receives a lot of attention due to its potential applications in many areas. However, many nice properties and fast algorithms for the unweighted version can not be extended to the weighted version. In this paper, we study the structural properties of this problem, giving some sufficient conditions for a vertex being or not being in a maximum weighted independent set. These properties provide a suite of reduction rules that includes and generalizes almost all frequently used reduction rules for this problem. These rules can efficiently find partial solutions and greatly reduce the instances, especially for sparse graphs. Based on them, we also propose a simple exact yet practical algorithm. To demonstrate the efficiency of our algorithm, we compare it with state-of-the-art algorithms on several well-known datasets from the real world. The experimental results reveal that our exact algorithm is not only faster than existing algorithms but also can exactly solve more hard instances with 1,000 seconds. For remaining infeasible instances, our reduction rules can also improve existing heuristic algorithms by producing higher-quality solutions using less time.

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Efficient Reductions and a Fast Algorithm of Maximum Weighted Independent Set
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cover image ACM Conferences

WWW '21: Proceedings of the Web Conference 2021

April 2021

4054 pages

ISBN:9781450383127

DOI:10.1145/3442381

Editors:
Jure Leskovec
Stanford
,
Marko Grobelnik
Jožef Stefan Institute
,
Marc Najork
Google
,
Jie Tang
Tsinghua University
,
Leila Zia
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Published: 03 June 2021

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Cited By

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https://dl.acm.org/doi/10.1016/j.cor.2024.106724
Liang YLiao CYi X(2023)A Primal-Dual Algorithmic Aspect of Link Scheduling in Dynamic Wireless Networks2023 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT54713.2023.10206777(2559-2564)Online publication date: 25-Jun-2023
https://doi.org/10.1109/ISIT54713.2023.10206777
Gedicke SArzoumanidis LHaunert J(2023)Automating the external placement of symbols for point features in situation maps for emergency responseCartography and Geographic Information Science10.1080/15230406.2023.221344650:4(385-402)Online publication date: 20-Jun-2023
https://doi.org/10.1080/15230406.2023.2213446
Gedicke SHaunert J(2023)An Empirical Study on Interfaces for Presenting Large Sets of Point Features in Mobile MapsThe Cartographic Journal10.1080/00087041.2023.218235460:1(25-42)Online publication date: 15-Aug-2023
https://doi.org/10.1080/00087041.2023.2182354
Xiao MHuang SChen X(2023)Maximum Weighted Independent Set: Effective Reductions and Fast Algorithms on Sparse GraphsAlgorithmica10.1007/s00453-023-01197-x86:5(1293-1334)Online publication date: 15-Dec-2023
https://doi.org/10.1007/s00453-023-01197-x

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