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- W331295377 abstract "Many large-scale real-world networks are well-known to have the power law distribution in their degree sequences: the number of vertices with degree i is proportional to $$i^{-beta }$$ for some constant $$beta $$ . It is a common belief that solving optimization problems in power-law graphs is easier. Unfortunately, many problems have been proven NP-hard, along with their inapproximability factors in power-law graphs. Therefore, it is of great importance to develop an algorithm framework such that these optimization problems can be approximated in power-law graphs, with provable theoretical approximation ratios. In this paper, we propose an algorithmic framework, called Low-Degree Percolation (LDP) Framework, for solving Minimum Dominating Set, Minimum Vertex Cover and Maximum Independent Set problems in power-law graphs. Using this framework, we further show a theoretical framework to derive the approximation ratios for these optimization problems in two well-known random power-law graphs. Our numerical analysis shows that, these optimization problems can be approximated into near 1 factor with high probability, using our proposed LDP algorithms, in power-law graphs with exponential factor $$beta ge 1.5$$ , which belongs to the range of most real-world networks." @default.
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- W331295377 date "2014-01-01" @default.
- W331295377 modified "2023-10-16" @default.
- W331295377 title "Approximation Algorithms for Optimization Problems in Random Power-Law Graphs" @default.
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- W331295377 doi "https://doi.org/10.1007/978-3-319-12691-3_26" @default.
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