@article{ChauhanFriedrichRothenberger2020,
  author    = {Chauhan, Ankit and Friedrich, Tobias and Rothenberger, Ralf},
  title     = {Greed is good for deterministic scale-free networks},
  series = {Algorithmica : an international journal in computer science},
  volume    = {82},
  journal   = {Algorithmica : an international journal in computer science},
  number    = {11},
  publisher = {Springer},
  address   = {New York},
  issn      = {0178-4617},
  doi       = {10.1007/s00453-020-00729-z},
  pages     = {3338 -- 3389},
  year      = {2020},
  abstract  = {Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach et al. (27th symposium on discrete algorithms (SODA), pp 1306-1325, 2016) introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U) and (2) power-law neighborhoods, that is, the degree distribution of neighbors of each vertex is also upper bounded by a power law (PLB-N). They showed that many real-world networks satisfy both properties and exploit them to design faster algorithms for a number of classical graph problems. We complement their work by showing that some well-studied random graph models exhibit both of the mentioned PLB properties. PLB-U and PLB-N hold with high probability for Chung-Lu Random Graphs and Geometric Inhomogeneous Random Graphs and almost surely for Hyperbolic Random Graphs. As a consequence, all results of Brach et al. also hold with high probability or almost surely for those random graph classes. In the second part we study three classical NP-hard optimization problems on PLB networks. It is known that on general graphs with maximum degree Delta, a greedy algorithm, which chooses nodes in the order of their degree, only achieves a Omega (ln Delta)-approximation forMinimum Vertex Cover and Minimum Dominating Set, and a Omega(Delta)-approximation forMaximum Independent Set. We prove that the PLB-U property with beta>2 suffices for the greedy approach to achieve a constant-factor approximation for all three problems. We also show that these problems are APX-hard even if PLB-U, PLB-N, and an additional power-law lower bound on the degree distribution hold. Hence, a PTAS cannot be expected unless P = NP. Furthermore, we prove that all three problems are in MAX SNP if the PLB-U property holds.},
  language  = {en}
}