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
| Hi-index | 5.23 |
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 E={e"1,e"2,...,e"n} of n elements. Each element e"i (i=1,...,n) has a positive cost c"i. A bundleb is a subset of E. We are also given a collection S={S"1,S"2,...,S"m} of m sets of bundles. More precisely, each set S"j (j=1,...,m) is composed of g(j) distinct bundles b"j^1,b"j^2,...,b"j^g^(^j^). A solution to mhsb is a subset E^'@?E such that for every S"j@?S at least one bundle is covered, i.e. b"j^l@?E^' for some l@?{1,2,...,g(j)}. The total cost of the solution, denoted by C(E^'), is @?"{"i"|"e"""i"@?"E"^"'"}c"i. The goal is to find a solution with a minimum total cost. We give a deterministic N(1-(1-1N)^M)-approximation algorithm, where N is the maximum number of bundles per set and M is the maximum number of sets in which an element can appear. 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-@e when N=3. It has to be noticed that the application of our algorithm in the case of the mink-sat problem matches the best known approximation ratio.