{"title":"弱次模化意味着本地化:受约束非次模块化函数最大化的局部搜索","authors":"","doi":"10.1016/j.disc.2024.114287","DOIUrl":null,"url":null,"abstract":"<div><div>Local search algorithms are commonly employed to address a variety of problems in the domain of operations research and combinatorial optimization. Most of the literature on the maximization of constrained monotone non-submodular functions is based on a greedy strategy, and few designs of local search approach are involved. In this paper, we explore the problem of maximizing a monotone non-submodular function under a <em>p</em>-matroid (<span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>) constraint with local search algorithms. And we indicate that weak submodularity implies localizability of set function optimization which can be used to offer provable approximation guarantees of local search algorithms.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weak submodularity implies localizability: Local search for constrained non-submodular function maximization\",\"authors\":\"\",\"doi\":\"10.1016/j.disc.2024.114287\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Local search algorithms are commonly employed to address a variety of problems in the domain of operations research and combinatorial optimization. Most of the literature on the maximization of constrained monotone non-submodular functions is based on a greedy strategy, and few designs of local search approach are involved. In this paper, we explore the problem of maximizing a monotone non-submodular function under a <em>p</em>-matroid (<span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>) constraint with local search algorithms. And we indicate that weak submodularity implies localizability of set function optimization which can be used to offer provable approximation guarantees of local search algorithms.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24004187\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24004187","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Weak submodularity implies localizability: Local search for constrained non-submodular function maximization
Local search algorithms are commonly employed to address a variety of problems in the domain of operations research and combinatorial optimization. Most of the literature on the maximization of constrained monotone non-submodular functions is based on a greedy strategy, and few designs of local search approach are involved. In this paper, we explore the problem of maximizing a monotone non-submodular function under a p-matroid () constraint with local search algorithms. And we indicate that weak submodularity implies localizability of set function optimization which can be used to offer provable approximation guarantees of local search algorithms.
期刊介绍:
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.