Covering the edges of bipartite graphs using K2,2 graphs
Theoretical Computer Science
Uniform unweighted set cover: The power of non-oblivious local search
Theoretical Computer Science
Tight approximation bounds for greedy frugal coverage algorithms
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
On the approximation ability of evolutionary optimization with application to minimum set cover
Artificial Intelligence
Packing-based approximation algorithm for the k-set cover problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A 6/5-approximation algorithm for the maximum 3-cover problem
Journal of Combinatorial Optimization
Tight approximation bounds for combinatorial frugal coverage algorithms
Journal of Combinatorial Optimization
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In the unweighted set cover problem we are given a set of elements $E=\{e_1,e_2,\ldots,e_n\}$ and a collection ${\cal F}$ of subsets of $E$. The problem is to compute a subcollection $SOL\subseteq{\cal F}$ such that $\bigcup_{S_j\in SOL}S_j=E$ and its size $|SOL|$ is minimized. When $|S|\leq k$ for all $S\in{\cal F}$, we obtain the unweighted $k$-set cover problem. It is well known that the greedy algorithm is an $H_k$-approximation algorithm for the unweighted $k$-set cover, where $H_k=\sum_{i=1}^k\frac{1}{i}$ is the $k$th harmonic number and that this bound on the approximation ratio of the greedy algorithm is tight for all constant values of $k$. Since the set cover problem is a fundamental problem, there is an ongoing research effort to improve this approximation ratio using modifications of the greedy algorithm. The previous best improvement of the greedy algorithm is an $(H_k-\frac{1}{2})$-approximation algorithm. In this paper we present a new $(H_k-\frac{196}{390})$-approximation algorithm for $k\geq4$ that improves the previous best approximation ratio for all values of $k\geq4$. Our algorithm is based on combining a local search during various stages of the greedy algorithm.