A generic algorithm for approximately solving stochastic graph optimization problems

Ei Ando, Hirotaka Ono, Masafumi Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a (directed or undirected) graph G = (V,E), a mutually independent random variable Xe obeying a normal distribution for each edge e ∈ E that represents its edge weight, and a property P on graph, a stochastic graph maximization problem asks the distribution function F MAX(x) of random variable XMAX = maxP∈P Σe∈A Xe, where property P is identified with the set of subgraphs P = (U,A) of G having P. This paper proposes a generic algorithm for computing an elementary function F̃(x) that approximates FMAX(x). It is applicable to any P and runs in time O(T AMAX(P)+TACNT(P)), provided the existence of an algorithm AMAX that solves the (deterministic) graph maximization problem for P in time TAMAX(P) and an algorithm ACNT that outputs an upper bound on |P| in time TACNT(P).We analyze the approximation ratio and apply it to three graph maximization problems. In case no efficient algorithms are known for solving the graph maximization problem for P, an approximation algorithm AAPR can be used instead of AMAX to reduce the time complexity, at the expense of increase of approximation ratio. Our algorithm can be modified to handle minimization problems.

Original languageEnglish
Title of host publicationStochastic Algorithms
Subtitle of host publicationFoundations and Applications - 5th International Symposium, SAGA 2009, Proceedings
Pages89-103
Number of pages15
DOIs
Publication statusPublished - Dec 1 2009
Event5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009 - Sapporo, Japan
Duration: Oct 26 2009Oct 28 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5792 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009
CountryJapan
CitySapporo
Period10/26/0910/28/09

Fingerprint

Optimization Problem
Graph in graph theory
Random variables
Elementary Functions
Approximation algorithms
Independent Random Variables
Normal distribution
Approximation
Undirected Graph
Directed Graph
Minimization Problem
Time Complexity
Distribution functions
Gaussian distribution
Approximation Algorithms
Subgraph
Distribution Function
Efficient Algorithms
Random variable
Upper bound

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ando, E., Ono, H., & Yamashita, M. (2009). A generic algorithm for approximately solving stochastic graph optimization problems. In Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings (pp. 89-103). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5792 LNCS). https://doi.org/10.1007/978-3-642-04944-6_8

A generic algorithm for approximately solving stochastic graph optimization problems. / Ando, Ei; Ono, Hirotaka; Yamashita, Masafumi.

Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. 2009. p. 89-103 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5792 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ando, E, Ono, H & Yamashita, M 2009, A generic algorithm for approximately solving stochastic graph optimization problems. in Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5792 LNCS, pp. 89-103, 5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009, Sapporo, Japan, 10/26/09. https://doi.org/10.1007/978-3-642-04944-6_8
Ando E, Ono H, Yamashita M. A generic algorithm for approximately solving stochastic graph optimization problems. In Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. 2009. p. 89-103. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-04944-6_8
Ando, Ei ; Ono, Hirotaka ; Yamashita, Masafumi. / A generic algorithm for approximately solving stochastic graph optimization problems. Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. 2009. pp. 89-103 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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