##### Date

2008

##### Collection title

Lecture Notes in Computer Science

##### Collection Id

5034

##### Dewey

Recherche opérationnelle

##### Sujet

approximation algorithm; min k −sat; minimum hitting set

##### Conference name

4th International Conference on Algorithmic Aspects in Information and Management (AAIM 2008)

##### Conference date

06-2008

##### Conference city

Shanghaï

##### Conference country

Chine

##### Book title

Algorithmic Aspects in Information and Management, 4th International Conference, AAIM 2008, Shanghai, China, June 23-25, 2008. Proceedings

##### Author

Fleischer, Rudolf; Xu, Jinhui

##### Publisher

springer

##### Publisher city

Berlin

##### Year

2008

##### ISBN

978-3-540-68865-5
##### Author

Angel, Eric

Bampis, Evripidis

Gourvès, Laurent

##### Type

Communication / Conférence

##### Item number of pages

3-14

##### Abstract (EN)

We consider a natural generalization of the classical minimum hitting set problem, the minimum hitting set of bundles problem (mhsb) which is defined as follows. We are given a set TeX of n elements. Each element e i (i = 1, ...,n) has a non negative cost c i . A bundle b is a subset of TeX . We are also given a collection TeX of m sets of bundles. More precisely, each set S j (j = 1, ..., m) is composed of g(j) distinct bundles TeX . A solution to mhsb is a subset TeX such that for every TeX at least one bundle is covered, i.e. TeX for some l ∈ {1,2, ⋯ ,g(j)}. The total cost of the solution, denoted by TeX , is TeX . The goal is to find a solution with minimum total cost.
We give a deterministic TeX -approximation algorithm, where N is the maximum number of bundles per set and M is 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 mhsb to the vertex cover problem, it implies that mhsb cannot be approximated within 1.36 when N = 2 and N − 1 − ε when N ≥ 3. It has to be noticed that the application of our algorithm in the case of the min k −sat problem matches the best known approximation ratio.