TY - GEN

T1 - A generic algorithm for approximately solving stochastic graph optimization problems

AU - Ando, Ei

AU - Ono, Hirotaka

AU - Yamashita, Masafumi

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78650651188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650651188&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-04944-6_8

DO - 10.1007/978-3-642-04944-6_8

M3 - Conference contribution

AN - SCOPUS:78650651188

SN - 3642049435

SN - 9783642049439

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 89

EP - 103

BT - Stochastic Algorithms

T2 - 5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009

Y2 - 26 October 2009 through 28 October 2009

ER -