Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
SIAM Journal on Discrete Mathematics
Improved non-approximability results for minimum vertex cover with density constraints
Theoretical Computer Science
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A 2-approximation algorithm for the minimum weight edge dominating set problem
Discrete Applied Mathematics
Approximating the dense set-cover problem
Journal of Computer and System Sciences
Approximating vertex cover on dense graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Improved approximation bounds for edge dominating set in dense graphs
Theoretical Computer Science
A $(2 - c \frac{\log {n}}{n})$ Approximation Algorithm for the Minimum Maximal Matching Problem
Approximation and Online Algorithms
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Connected vertex covers in dense graphs
Theoretical Computer Science
Minimum maximal matching is NP-hard in regular bipartite graphs
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A tight analysis of the maximal matching heuristic
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
| Hi-index | 5.23 |
We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere @e-dense and average @e@?-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem. As a direct result, we obtain for the special case of the Minimum Edge Dominating Set problem in everywhere @e-dense and average @e@?-dense graphs by using the techniques of Karpinski and Zelikovsky, the approximation ratios of min{2,3/(1+2@e)} and of min{2,3/(3-21-@e@?)}, respectively. On the other hand, we give new approximation lower bounds for the Minimum Edge Dominating Set problem in dense graphs. Assuming the Unique Game Conjecture, we show that it is NP-hard to approximate the Minimum Edge Dominating Set problem in everywhere @e-dense graphs with a ratio better than 2/(1+@e) with @e1/3 and 2/(2-1-@e@?) with @e@?5/9 in average @e@?-dense graphs.