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

Ei Ando, Shuji Kijima

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Computing high dimensional volumes is a hard problem, even for approximation. Several randomized approximation techniques for #P-hard problems have been developed in the three decades, while some deterministic approximation algorithms are recently developed only for a few #P-hard problems. Motivated by a new technique for a deterministic approximation, this paper is concerned with the volume computation of 0-1 knapsack polytopes, which is known to be #P-hard. This paper presents a new technique based on approximate convolutions for a deterministic approximation of volume computations, and provides a fully polynomial-time approximation scheme for the volume computation of 0-1 knapsack polytopes. We also give an extension of the result to multi-constrained knapsack polytopes with a constant number of constraints.

Original languageEnglish
Pages (from-to)1245-1263
Number of pages19
JournalAlgorithmica
Volume76
Issue number4
DOIs
Publication statusPublished - Dec 1 2016

Fingerprint

FPTAS
Knapsack
Polytopes
Convolution
Approximation
Approximation algorithms
Fully Polynomial Time Approximation Scheme
Deterministic Algorithm
Polynomials
Approximation Algorithms
High-dimensional
Computing

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

An FPTAS for the Volume Computation of 0-1 Knapsack Polytopes Based on Approximate Convolution. / Ando, Ei; Kijima, Shuji.

In: Algorithmica, Vol. 76, No. 4, 01.12.2016, p. 1245-1263.

Research output: Contribution to journalArticle

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