Computational complexity arising from degree correlations in networks
无序系统与神经网络
2009-11-07 v2 统计力学
计算复杂性
摘要
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of finding minimal vertex covers on these graphs, we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks. This results in a higher complexity of the network in a computational sense: Simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case, whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization.
引用
@article{arxiv.cond-mat/0207035,
title = {Computational complexity arising from degree correlations in networks},
author = {Alexei Vazquez and Martin Weigt},
journal= {arXiv preprint arXiv:cond-mat/0207035},
year = {2009}
}
备注
4 pages, 1 figure, accepted in Phys. Rev. E