通过分区计算逼近子集和比率

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Acta Informatica Pub Date : 2024-01-12 DOI:10.1007/s00236-023-00451-7
Giannis Alonistiotis, Antonis Antonopoulos, Nikolaos Melissinos, Aris Pagourtzis, Stavros Petsalakis, Manolis Vasilakis
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引用次数: 0

摘要

我们针对子集和比问题提出了一种新的 FPTAS,在给定一个整数集合的情况下,要求找出两个不相交的子集,使它们的和之比尽可能接近 1。我们的方案利用了分治的精确算法和近似算法,清楚地展示了这两个算法问题之间的密切关系。根据输入集 n 的大小与误差幅度 \(\varepsilon \)之间的关系,我们改进了 Melissinos 和 Pagourtzis [COCOON 2018] 目前已知的最佳算法,其复杂度为 \(\mathcal {O} (n^4 / \varepsilon )\)。特别是,在我们提出的方案中,n 的指数可能会下降到 2,这取决于所使用的 Partition 算法。
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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.

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来源期刊
Acta Informatica
Acta Informatica 工程技术-计算机:信息系统
CiteScore
2.40
自引率
16.70%
发文量
24
审稿时长
>12 weeks
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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