DEAMON: energy-efficient sensor monitoring
SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
Uniform unweighted set cover: The power of non-oblivious local search
Theoretical Computer Science
On the approximation ability of evolutionary optimization with application to minimum set cover
Artificial Intelligence
Approximating the unweighted k-set cover problem: greedy meets local search
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Greedy heuristics with regret, with application to the cheapest insertion algorithm for the TSP
Operations Research Letters
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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In the weighted 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 $E$, where each $S \in \cal F$ has a positive cost $c_{S}$. The problem is to compute a subcollection $SOL$ such that $\bigcup_{S\in SOL}S_j=E$ and its cost $\sum_{S\in SOL}c_S$ is minimized. When $|S|\le k\ \forall S\in\cal F$ we obtain the weighted $k$-set cover problem. It is well known that the greedy algorithm is an $H_k$-approximation algorithm for the weighted $k$ set cover, where $H_k=\sum_{i=1}^k {1 \over i}$ is the $k$th harmonic number, and that this bound is exact for the greedy algorithm for all constant values of $k$. In this paper we give the first improvement on this approximation ratio for all constant values of $k$. This result shows that the greedy algorithm is not the best possible for approximating the weighted set cover problem. Our method is a modification of the greedy algorithm that allows the algorithm to regret.