Approximation Algorithms for Optimization Problems in Random Power-Law Graphs

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.

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