ACM Transactions on Database Systems (TODS)
The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
On approximation algorithms for the minimum satisfiability problem
Information Processing Letters
Approximation algorithms
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Dynamic programming solution for multiple query optimization problem
Information Processing Letters
Approximating MIN 2-SAT and MIN 3-SAT
Theory of Computing Systems
On dependent randomized rounding algorithms
Operations Research Letters
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We consider a natural generalization of the classical minimum hitting setproblem, the minimum hitting set of bundlesproblem (mhsb) which is defined as follows. We are given a set $\mathcal{E}=\{e_1, e_2 , \ldots , e_n\}$ of nelements. Each element ei(i= 1, ...,n) has a non negative cost ci. A bundlebis a subset of $\mathcal{E}$. We are also given a collection $\mathcal{S}=\{S_1, S_2 , \ldots , S_m\}$ of msets of bundles. More precisely, each set Sj(j= 1, ..., m) is composed of g(j) distinct bundles $b_j^1, b_j^2, \ldots , b_j^{g(j)}$. A solution to mhsbis a subset $\mathcal{E}' \subseteq \mathcal{E}$ such that for every $S_j \in \mathcal{S}$ at least one bundle is covered, i.e. $b_j^l \subseteq \mathcal{E}'$ for some l驴 {1,2, 驴 ,g(j)}. The total costof the solution, denoted by $C(\mathcal{E'})$, is $\sum_{\{i \mid e_i \in \mathcal{E'}\}} c_i$. The goal is to find a solution with minimumtotal cost.We give a deterministic $N(1-(1-\frac{1}{N})^M)$-approximation algorithm, where Nis the maximum number of bundles per set and Mis the maximum number of sets an element can appear in. This is roughly speaking the best approximation ratio that we can obtain since, by reducing mhsbto the vertex cover problem, it implies that mhsbcannot be approximated within 1.36 when N= 2 and N驴 1 驴 驴when N驴 3. It has to be noticed that the application of our algorithm in the case of the mink驴satproblem matches the best known approximation ratio.