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Computational complexity arising from degree correlations in networks | | Alexei Vazquez
; Martin Weigt
; | | Date: |
1 Jul 2002 | | Journal: | Phys. Rev. E 67, 027101 (2003) | | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics; Computational Complexity | cond-mat.dis-nn cond-mat.stat-mech cs.CC | | Abstract: | 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. | | Source: | arXiv, cond-mat/0207035 | | Other source: | [GID 11935] pmid12636856 | | Services: | Forum | Review | PDF | Favorites | |
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