On the Hardness of Optimization in Power Law Graphs

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 exhibit a power-law distribution: the number of nodes yi of a given degree i is proportional to i−β where β > 0 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 β? 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 β. In particular, we show that some classical problems, such as CLIQUE

• Type: Conference
• Year: 2007
• Where: COCOON
• Authors: Alessandro Ferrante, Gopal Pandurangan, Kihong Park
• Keywords: COCOON 2007, Combinatorial Optimization, Large-scale Real-world Graphs, Power-law Graphs