An FPTAS for the Volume Computation of 0-1 Knapsack Polytopes Based on Approximate Convolution Integral

Ei Ando, Shuji Kijima

研究成果: Chapter in Book/Report/Conference proceedingChapter

2 引用 (Scopus)

抜粋

Computing high dimensional volumes is a hard problem, even for approximation. It is known that no polynomial-time deterministic algorithm can approximate with ratio 1.999n the volumes of convex bodies in the n dimension as given by membership oracles. Several randomized approximation techniques for #P-hard problems has been developed in the three decades, while some deterministic approximation algorithms are recently developed only for a few #P-hard problems. For instance, Stefankovic, Vempala and Vigoda (2012) gave an FPTAS for counting 0-1 knapsack solutions (i.e., integer points in a 0-1 knapsack polytope) based on an ingenious dynamic programming. Motivated by a new technique for designing FPTAS for #P-hard problems, this paper is concerned with the volume computation of 0-1 knapsack polytopes: it is given by {x (Formula presented.)} with a positive integer vector a and a positive integer b as an input, the volume computation of which is known to be #P-hard. Li and Shi (2014) gave an FPTAS for the problem by modifying the dynamic programming for counting solutions. This paper presents a new technique based on approximate convolution integral for a deterministic approximation of volume computations, and provides an FPTAS for the volume computation of 0-1 knapsack polytopes.

元の言語英語
ホスト出版物のタイトルAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
編集者Hee-Kap Ahn, Chan-Su Shin
出版者Springer Verlag
ページ376-386
ページ数11
ISBN(電子版)9783319130743
DOI
出版物ステータス出版済み - 1 1 2014

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
8889
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • これを引用

    Ando, E., & Kijima, S. (2014). An FPTAS for the Volume Computation of 0-1 Knapsack Polytopes Based on Approximate Convolution Integral. : H-K. Ahn, & C-S. Shin (版), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings (pp. 376-386). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 8889). Springer Verlag. https://doi.org/10.1007/978-3-319-13075-0_30