Inclusion and exclusion algorithm for the Hamiltonian Path Problem
Information Processing Letters
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
Approximation algorithms
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Exact and approximate link scheduling algorithms under the physical interference model
Proceedings of the fifth international workshop on Foundations of mobile computing
The Travelling Salesman Problem in Bounded Degree Graphs
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Dynamic programming meets the principle of inclusion and exclusion
Operations Research Letters
Exact Algorithms for Set Multicover and Multiset Multicover Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Dynamic programming based algorithms for set multicover and multiset multicover problems
Theoretical Computer Science
| Hi-index | 5.23 |
Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusion-exclusion principle. The presented ESMC (Exact Set Multi-Covering) algorithm takes O^*((2t)^n) time and O^*((t+1)^n) space where t is the maximum value in the coverage requirement set (The O^*(f(n)) notation omits a polylog(f(n)) factor). We also propose the other three exact algorithms through different tradeoffs of the time and space complexities. To the best of our knowledge, this present paper is the first one to give exact algorithms for the set multi-covering problem with nontrivial time and space complexities. This paper can also be regarded as a generalization of the exact algorithm for the set covering problem given in [A. Bjorklund, T. Husfeldt, M. Koivisto, Set partitioning via inclusion-exclusion, SIAM Journal on Computing, in: FOCS 2006 (in press, special issue)].