Approximation of k-set cover by semi-local optimization
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
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Approximation algorithms
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
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
Approximating the Spanning k-Tree Forest Problem
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
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
An improved approximation algorithm for spanning star forest in dense graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
On the approximation of computing evolutionary trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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A star forest is a collection of vertex-disjoint trees of depth at most 1, and its size is the number of leaves in all its components. A spanning star forest of a given graph G is a spanning subgraph of G that is also a star forest. The spanning star forest problem (SSF for short) [14] is to find the maximum-size spanning star forest of a given graph. In this paper, we study several variants of SSF, obtaining first or improved approximation and hardness results in all settings as shown below. 1. We study SSF on graphs of minimum degree δ(n), n being the number of vertices in the input graph. Call this problem (≥ δ(n))-SSF. We give an (almost) complete characterization of the complexity of (≥ δ(n))-SSF with respect to δ(n) as follows. - When 1 ≤ δ(n) ≤ O(1), (≥ δ(n))-SSF is APX-complete. - When ω(1) ≤ δ(n) ≤ O(n1-ε) for some constant ε 0, (≥ δ(n))- SSF is NP-hard but admits a PTAS. - When δ(n) ≥ ω(n1-ε) for every constant ε 0, (≥ δ(n))-SSF is not NP-hard assuming Exponential Time Hypothesis (ETH). 2. We investigate the spanning k-tree forest problem, which is a natural generalization of SSF. We obtain the first inapproximability bound of 1 - ω(1/k) for this problem, which asymptotically matches the known approximation ratio of 1 - 1/k+1 given in [13]. We then propose an approximation algorithm for it with a slightly improved approximation ratio of 1 - 1/k+2. 3. We prove that SSF cannot be approximated to any factor larger than 244/245 in polynomial time, unless P = NP. This improves the previously best known bound of 259/260 [14].