A Mildly Exponential Time Algorithm for Approximating the Number of Solutions to a Multidimensional Knapsack Problem

Author:

Dyer Martin,Frieze Alan,Kannan Ravi,Kapoor Ajai,Perkovic Ljubomir,Vazirani Umesh

Abstract

We describe a time randomized algorithm that estimates the number of feasible solutions of a multidimensional knapsack problem within 1 ± ε of the exact number. (Here r is the number of constraints and n is the number of integer variables.) The algorithm uses a Markov chain to generate an almost uniform random solution to the problem.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Reference15 articles.

1. Approximate counting, uniform generation and rapidly mixing Markov chains

2. How hard is it to marry at random?;Broder;Proceedings of the 18th Annual ACM Symposium on Theory of Computing,1986

3. A mildly exponential approximation algorithm for the permanent

4. On the number of Euler orientations of a graph;Mihail;Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms,1992

Cited by 23 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Discrete Optimal Transport with Independent Marginals is #P-Hard;SIAM Journal on Optimization;2023-06-01

2. Estimation of the Size of Union of Delphic Sets: Achieving Independence from Stream Size;Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems;2022-06-12

3. Mining Statistically Significant Communities from Weighted Networks;IEEE Transactions on Knowledge and Data Engineering;2022

4. Computation of Exact Bootstrap Confidence Intervals: Complexity and Deterministic Algorithms;Operations Research;2020-05

5. Faster FPTASes for counting and random generation of Knapsack solutions;Information and Computation;2019-08

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3