SIAM Journal on Discrete Mathematics
Edge domination on bipartite permutation graphs and cotriangulated graphs
Information Processing Letters
A 2-approximation algorithm for the minimum weight edge dominating set problem
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
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
Approximating vertex cover on dense graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A tight analysis of the maximal matching heuristic
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Facet defining inequalities among graph invariants: The system GraPHedron
Discrete Applied Mathematics
Connected Vertex Covers in Dense Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
A $(2 - c \frac{\log {n}}{n})$ Approximation Algorithm for the Minimum Maximal Matching Problem
Approximation and Online Algorithms
Connected vertex covers in dense graphs
Theoretical Computer Science
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We analyze the simple greedy algorithm that iteratively removes the endpoints of a maximum-degree edge in a graph, where the degree of an edge is the sum of the degrees of its endpoints. This algorithm provides a 2-approximation to the minimum edge dominating set and minimum maximal matching problems. We refine its analysis and give an expression of the approximation ratio that is strictly less than 2 in the cases where the input graph has n vertices and at least $\epsilon \binom{n}{2}$ edges, for ε 1/2. This ratio is shown to be asymptotically tight for ε 1/2.