TY - GEN

T1 - Approximating the statistics of various properties in randomly weighted graphs

AU - Emek, Yuval

AU - Korman, Amos

AU - Shavitt, Yuval

PY - 2011

Y1 - 2011

N2 - Consider the setting of randomly weighted graphs, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, weighted graph properties such as the diameter, the radius (with respect to a designated vertex), and the weight of a minimum spanning tree become random variables and we are interested in computing their expectation. Unfortunately, this turns out to be #P-hard. In this paper, we define a family of weighted graph properties (that includes the above three) and show that for each property in this family, the problem of computing the kth moment (and in particular, the expectation) of the corresponding random variable admits a fully polynomial-time randomized approximation scheme (FPRAS) for every fixed k.

AB - Consider the setting of randomly weighted graphs, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, weighted graph properties such as the diameter, the radius (with respect to a designated vertex), and the weight of a minimum spanning tree become random variables and we are interested in computing their expectation. Unfortunately, this turns out to be #P-hard. In this paper, we define a family of weighted graph properties (that includes the above three) and show that for each property in this family, the problem of computing the kth moment (and in particular, the expectation) of the corresponding random variable admits a fully polynomial-time randomized approximation scheme (FPRAS) for every fixed k.

UR - http://www.scopus.com/inward/record.url?scp=79955725164&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973082.113

DO - 10.1137/1.9781611973082.113

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AN - SCOPUS:79955725164

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1455

EP - 1467

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

PB - Association for Computing Machinery

ER -