Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Size bounds for dynamic monopolies
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Local Majority Voting, Small Coalitions and Controlling Monopolies in Graphs: A Review
Local Majority Voting, Small Coalitions and Controlling Monopolies in Graphs: A Review
Probabilistic local majority voting for the agreement problem on finite graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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Given a graph G = (V, E) and a set of vertices M ⊆ V, a vertex v ∈ V is said to be controlled by M if the majority of v's neighbors (including itself) belongs to M. M is called a monopoly if every vertex v ∈ V is controlled by M. For a specified M and a range for E (E1 ⊆ E ⊆ E2), we try to determine E such that M is a monopoly in G = (V, E). We first present a polynomial algorithm for testing if such an E exists, by formulating it as a network flow problem. Assuming that a solution E does exist, we then show that a solution with the maximum or minimum |E| can be found in polynomial time, by considering them as weighted matching problems. In case there is no solution E, we want to maximize the number of vertices controlled by the given M. Unfortunately, this problem turns out to be NP-hard. We therefore design a simple approximation algorithm which guarantees an approximation ratio of 2.