On approximating the minimum independent dominating set
Information Processing Letters
SIAM Journal on Discrete Mathematics
Approximating the minimum maximal independence number
Information Processing Letters
Approximating the tree and tour covers of a graph
Information Processing Letters
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
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
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Improved approximations for tour and tree covers
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Structure in Approximation Classes (Extended Abstract)
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
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We investigate polynomial-time approximability of the problems related to edge dominating sets of graphs. When edges are unit-weighted, the edge dominating set problem is polynomially equivalent to the minimum maximal matching problem, in either exact or approximate computation, and the former problem was recently found to be approximable within a factor of 2 even with arbitrary weights. It will be shown, in contrast with this, that the minimum weight maximal matching problem cannot be approximated within any polynomially computable factor unless P=NP. The connected edge dominating set problem and the connected vertex cover problem also have the same approximability when edges/vertices are unit-weighted, and the former problem is known to be approximable, even with general edge weights, within a factor of 3.55. We will show that, when general weights are allowed, 1) the connected edge dominating set problem can be approximated within a factor of 3 + Ɛ, and 2) the connected vertex cover problem is approximable within a factor of ln n + 3 but cannot be within (1 - Ɛ) ln n for any Ɛ 0 unless NP ⊂ DTIME(nO(log log n)).