Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
Approximation algorithms
Approximating vertex cover on dense graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Spanning Star Forest Problem and Its Application to Genomic Sequence Alignment
SIAM Journal on Computing
Improved Approximation Algorithms for the Spanning Star Forest Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Improved approximation bounds for edge dominating set in dense graphs
Theoretical Computer Science
An Improved Approximation Bound for Spanning Star Forest and Color Saving
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Exponential time algorithms for the minimum dominating set problem on some graph classes
ACM Transactions on Algorithms (TALG)
On the approximation of computing evolutionary trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On variants of the spanning star forest problem
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
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A spanning subgraph of a given graph G is called a spanning star forest of G if it is a collection of node-disjoint trees of depth at most 1 (such trees are called stars). The size of a spanning star forest is the number of leaves in all its components. The goal of the spanning star forest problem [12] is to find the maximum-size spanning star forest of a given graph. In this paper, we study this problem in c-dense graphs, where for c ε (0, 1), a graph of n vertices is called c-dense if it contains at least cn2/2 edges [2]. We design a (α+(1-α)√c-ε)-approximation algorithm for spanning star forest in c-dense graphs for any ε 0, where α = 193/240 is the best known approximation ratio of the spanning star forest problem in general graphs [3]. Thus, our approximation ratio outperforms the best known bound for this problem when dealing with c-dense graphs. We also prove that for any c ε (0, 1), there is a constant ε = ε(c) 0 such that approximating spanning star forest in c-dense graphs within a factor of 1 - ε is NP-hard. We then demonstrate that for weighted versions (both node- and edge- weighted) of this problem, we cannot get any approximation algorithm with strictly better performance guarantee in c-dense graphs than that of the best possible approximation algorithm for general graphs. Finally, we give strong hardness-of-approximation results for a closely related problem, the minimum dominating set problem, in c-dense graphs.