Optimal File Sharing in Distributed Networks
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Linear Time Algorithms on Chordal Bipartite and Strongly Chordal Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Hardness of Approximating Minimum Monopoly Problems
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Information Processing Letters
Hardness results and approximation algorithms of k-tuple domination in graphs
Information Processing Letters
On Dominating Sets and Independent Sets of Graphs
Combinatorics, Probability and Computing
On the submodularity of influence in social networks
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximation hardness of dominating set problems in bounded degree graphs
Information and Computation
k-tuple total domination in graphs
Discrete Applied Mathematics
On positive influence dominating sets in social networks
Theoretical Computer Science
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the approximability and exact algorithms for vector domination and related problems in graphs
Discrete Applied Mathematics
On the approximability of positive influence dominating set in social networks
Journal of Combinatorial Optimization
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We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S has a prescribed number of neighbors in S. In total vector domination, the requirement is extended to all vertices of the graph. We prove that these problems cannot be approximated to within a factor of clogn, for suitable constants c, unless every problem in NP is solvable in slightly super-polynomial time. We also show that two natural greedy strategies have approximation factors O(logΔ(G)), where Δ(G) is the maximum degree of the graph G. We also provide exact polynomial time algorithms for several classes of graphs. Our results extend, improve, and unify several results previously known in the literature.