Zhihua Huang, An Zhang, Mingqi Gao, Jiayi Sun, Yong Chen
{"title":"Approximation algorithms for the k+-star packing problem","authors":"Zhihua Huang, An Zhang, Mingqi Gao, Jiayi Sun, Yong Chen","doi":"10.1016/j.orl.2025.107249","DOIUrl":null,"url":null,"abstract":"<div><div>Given a target graph <em>G</em> and a set <span><math><mi>G</mi></math></span> of <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-stars, that is, stars with at least <em>k</em> satellites, a <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-star packing of <em>G</em> is a set of vertex-disjoint subgraphs of <em>G</em> with each isomorphic to some element of <span><math><mi>G</mi></math></span>. The <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-star packing problem is to find one such packing that covers as many vertices of <em>G</em> as possible. It is known to be NP-hard for any fixed <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>, and has a simple 2-approximation algorithm when <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>. In this paper, we present an improved algorithm with a tight approximation ratio of 9/5 for <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, and a <span><math><mfrac><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>-approximation algorithm for general <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> using the local search approach.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107249"},"PeriodicalIF":0.8000,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637725000100","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Given a target graph G and a set of -stars, that is, stars with at least k satellites, a -star packing of G is a set of vertex-disjoint subgraphs of G with each isomorphic to some element of . The -star packing problem is to find one such packing that covers as many vertices of G as possible. It is known to be NP-hard for any fixed , and has a simple 2-approximation algorithm when . In this paper, we present an improved algorithm with a tight approximation ratio of 9/5 for , and a -approximation algorithm for general using the local search approach.
期刊介绍:
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.