{"title":"通过分区计算逼近子集和比率","authors":"Giannis Alonistiotis, Antonis Antonopoulos, Nikolaos Melissinos, Aris Pagourtzis, Stavros Petsalakis, Manolis Vasilakis","doi":"10.1007/s00236-023-00451-7","DOIUrl":null,"url":null,"abstract":"<div><p>We present a new FPTAS for the <span>Subset Sum Ratio</span> problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to 1 as possible. Our scheme makes use of exact and approximate algorithms for <span>Partition</span>, and clearly showcases the close relationship between the two algorithmic problems. Depending on the relationship between the size of the input set <i>n</i> and the error margin <span>\\(\\varepsilon \\)</span>, we improve upon the best currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of complexity <span>\\(\\mathcal {O} (n^4 / \\varepsilon )\\)</span>. In particular, the exponent of <i>n</i> in our proposed scheme may decrease down to 2, depending on the <span>Partition</span> algorithm used.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-023-00451-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Approximating subset sum ratio via partition computations\",\"authors\":\"Giannis Alonistiotis, Antonis Antonopoulos, Nikolaos Melissinos, Aris Pagourtzis, Stavros Petsalakis, Manolis Vasilakis\",\"doi\":\"10.1007/s00236-023-00451-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a new FPTAS for the <span>Subset Sum Ratio</span> problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to 1 as possible. Our scheme makes use of exact and approximate algorithms for <span>Partition</span>, and clearly showcases the close relationship between the two algorithmic problems. Depending on the relationship between the size of the input set <i>n</i> and the error margin <span>\\\\(\\\\varepsilon \\\\)</span>, we improve upon the best currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of complexity <span>\\\\(\\\\mathcal {O} (n^4 / \\\\varepsilon )\\\\)</span>. In particular, the exponent of <i>n</i> in our proposed scheme may decrease down to 2, depending on the <span>Partition</span> algorithm used.</p></div>\",\"PeriodicalId\":7189,\"journal\":{\"name\":\"Acta Informatica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00236-023-00451-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Informatica\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00236-023-00451-7\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Informatica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00236-023-00451-7","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Approximating subset sum ratio via partition computations
We present a new FPTAS for the Subset Sum Ratio problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to 1 as possible. Our scheme makes use of exact and approximate algorithms for Partition, and clearly showcases the close relationship between the two algorithmic problems. Depending on the relationship between the size of the input set n and the error margin \(\varepsilon \), we improve upon the best currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of complexity \(\mathcal {O} (n^4 / \varepsilon )\). In particular, the exponent of n in our proposed scheme may decrease down to 2, depending on the Partition algorithm used.
期刊介绍：
Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics.
Topics of interest include:
• semantics of programming languages
• models and modeling languages for concurrent, distributed, reactive and mobile systems
• models and modeling languages for timed, hybrid and probabilistic systems
• specification, program analysis and verification
• model checking and theorem proving
• modal, temporal, first- and higher-order logics, and their variants
• constraint logic, SAT/SMT-solving techniques
• theoretical aspects of databases, semi-structured data and finite model theory
• theoretical aspects of artificial intelligence, knowledge representation, description logic
• automata theory, formal languages, term and graph rewriting
• game-based models, synthesis
• type theory, typed calculi
• algebraic, coalgebraic and categorical methods
• formal aspects of performance, dependability and reliability analysis
• foundations of information and network security
• parallel, distributed and randomized algorithms
• design and analysis of algorithms
• foundations of network and communication protocols.
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