On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Handbook of Graphs and Networks: From the Genome to the Internet
Handbook of Graphs and Networks: From the Genome to the Internet
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Conductance and congestion in power law graphs
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Structural and algorithmic aspects of massive social networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Graph Theory With Applications
Graph Theory With Applications
On the hardness of optimization in power-law graphs
Theoretical Computer Science
Approximation hardness of dominating set problems in bounded degree graphs
Information and Computation
Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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The remarkable discovery of many large-scale real networks is the power-law distribution in degree sequence: the number of vertices with degree i is proportional to i^-^@b for some constant @b1. A lot of researchers believe that it may be easier to solve some optimization problems in power-law graphs. Unfortunately, many problems have been proved NP-hard even in power-law graphs. Intuitively, a theoretical question is raised: are these problems on power-law graphs still as hard as on general graphs? In this paper, we show that many optimal substructure problems, such as Minimum Dominating Set, Minimum Vertex Cover and Maximum Independent Set, are easier to solve in power-law graphs by illustrating better inapproximability factors. An optimization problem has the property of optimal substructure if its optimal solution on some given graph is essentially the union of the optimal sub-solutions on all maximal connected components. In particular, we prove the above problems and a more general problem (@r-Minimum Dominating Set) remain APX-hard and their constant inapproximability factors on general power-law graphs by using the cycle-based embedding technique to embed any d-bounded graphs into a power-law graph. In addition, in simple power-law graphs, we further prove the corresponding inapproximability factors of these problems based on the graphic embedding technique as well as that of Maximum Clique and Minimum Coloring using the embedding technique in [1]. As a result of these inapproximability factors, the belief that there exists some (1+o(1))-approximation algorithm for these problems on power-law graphs is proven to be not always true. At last, we do in-depth investigations in the relationship between the exponential factor @b and constant greedy approximation algorithms.