分支定界法求解子集和问题若干实例的最优性和复杂性分析

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-12-17 DOI:10.1515/comp-2020-0212

R. Kolpakov, M. Posypkin

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引用次数: 0

摘要

摘要本文研究了布尔背包问题的一个特例——子集和问题的分支定界法的一个变种的并行化问题。以下是解决这个问题的自然方法。在第一阶段，其中一个处理器（控制处理器）执行一定数量的算法步骤来解决给定问题，同时生成该问题的一定数量的子问题。在第二阶段，生成的子问题被发送到其他处理器进行求解（每个处理器一个子问题）。处理器完全解决接收到的子问题，并将它们的解返回给控制处理器，控制处理器从这些解中选择初始问题的最优解。对于这种方法，我们正式定义了并行计算的模型（前沿并行化方案）和前沿方案的复杂性概念。我们研究了子集和问题的两个特殊情况下，前沿格式复杂性的渐近行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimality and Complexity Analysis of a Branch-and-Bound Method in Solving Some Instances of the Subset Sum Problem

Abstract In this paper we study the question of parallelization of a variant of Branch-and-Bound method for solving of the subset sum problem which is a special case of the Boolean knapsack problem. The following natural approach to the solution of this question is considered. At the first stage one of the processors (control processor) performs some number of algorithm steps of solving a given problem with generating some number of subproblems of the problem. In the second stage the generated subproblems are sent to other processors for solving (one subproblem per processor). Processors solve completely the received subproblems and return their solutions to the control processor which chooses the optimal solution of the initial problem from these solutions. For this approach we define formally a model of parallel computing (frontal parallelization scheme) and the notion of complexity of the frontal scheme. We study the asymptotic behavior of the complexity of the frontal scheme for two special cases of the subset sum problem.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.