A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Conductance and congestion in power law graphs
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On Certain Connectivity Properties of the Internet Topology
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
Positive Influence Dominating Set in Online Social Networks
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Modeling and Designing Real---World Networks
Algorithmics of Large and Complex Networks
On positive influence dominating sets in social networks
Theoretical Computer Science
On the hardness and inapproximability of optimization problems on power law graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The complexity and approximability of minimum contamination problems
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
New techniques for approximating optimal substructure problems in power-law graphs
Theoretical Computer Science
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
On the discovery of critical links and nodes for assessing network vulnerability
IEEE/ACM Transactions on Networking (TON)
Approximability of the vertex cover problem in power-law graphs
Theoretical Computer Science
On the approximability of positive influence dominating set in social networks
Journal of Combinatorial Optimization
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Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks appear to exhibit a power-law distribution: the number of nodes y"i of a given degree i is proportional to i^-^@b where @b0 is a constant that depends on the application domain. There is practical evidence that combinatorial optimization in power-law graphs is easier than in general graphs, prompting the basic theoretical question: Is combinatorial optimization in power-law graphs easy? Does the answer depend on the power-law exponent @b? Our main result is the proof that many classical NP-hard graph-theoretic optimization problems remain NP-hard on power-law graphs for certain values of @b. In particular, we show that some classical problems, such as CLIQUE and COLORING, remain NP-hard for all @b=1. Moreover, we show that all the problems that satisfy the so-called ''optimal substructure property'' remain NP-hard for all @b0. This includes classical problems such as MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, and MINIMUM DOMINATING SET. Our proofs involve designing efficient algorithms for constructing graphs with prescribed degree sequences that are tractable with respect to various optimization problems.