Average-Case Complexity of the Min-Sum Matrix Product Problem

Research output: Chapters, Conference Papers, Creative and Literary Works (RGC: 12, 32, 41, 45)32_Refereed conference paper (with ISBN/ISSN)

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Detail(s)

Original languageEnglish
Title of host publicationAlgorithms and Computation
EditorsHee-Kap Ahn, Chan-Su Shin
PublisherSpringer
Pages41-52
ISBN (Electronic)9783319130750
ISBN (Print)9783319130743
Publication statusPublished - Dec 2014

Publication series

NameLecture Notes in Computer Science
Volume8889
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Title25th International Symposium on Algorithms and Computation (ISAAC 2014)
Location
PlaceKorea, Republic of
CityJeonju
Period15 - 17 December 2014

Abstract

We study the average-case complexity of min-sum product of matrices, which is a fundamental operation that has many applications in computer science. We focus on optimizing the number of “algebraic” operations (i.e., operations involving real numbers) used in the computation, since such operations are usually expensive in various environments. We present an algorithm that can compute the min-sum product of two ×n real matrices using only (n2) algebraic operations, given that the matrix elements are drawn independently and identically from some fixed probability distribution satisfying several constraints. This improves the previously best known upper-bound of (n2 log n). The class of probability distributions under which our algorithm works include many important and commonly used distributions, such as uniform distributions, exponential distributions, and folded normal distributions. In order to evaluate the performance of the proposed algorithm, we performed experiments to compare the running time of the proposed algorithm with algorithms in[7]. The experimental results demonstrate that our algorithm achieves significant performance improvement over the previous algorithms.

Citation Format(s)

Average-Case Complexity of the Min-Sum Matrix Product Problem. / Fong, Ken; Li, Minming; Liang, Hongyu; Yang, Linji; Yuan, Hao.

Algorithms and Computation. ed. / Hee-Kap Ahn; Chan-Su Shin. Springer, 2014. p. 41-52 (Lecture Notes in Computer Science; Vol. 8889).

Research output: Chapters, Conference Papers, Creative and Literary Works (RGC: 12, 32, 41, 45)32_Refereed conference paper (with ISBN/ISSN)