A generic algorithm for approximately solving stochastic graph optimization problems

  • Authors:

  • Ei Ando;Hirotaka Ono;Masafumi Yamashita

  • Affiliations:

  • Dept. Computer Sci. and Communication Eng., Kyushu University, Fukuoka, Fukuoka, Japan;Dept. Computer Sci. and Communication Eng., Kyushu University, Fukuoka, Fukuoka, Japan and Institute of Systems, Information Technologies and Nanotechnologies, Fukuoka, Fukuoka, Japan;Dept. Computer Sci. and Communication Eng., Kyushu University, Fukuoka, Fukuoka, Japan and Institute of Systems, Information Technologies and Nanotechnologies, Fukuoka, Fukuoka, Japan

  • Venue:
  • SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
  • Year:
  • 2009

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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 FMAX(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 F(x) that approximates FMAX(x). It is applicable to any P and runs in time O(TAMAX(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.