Greedy algorithmsNP-HardSet cover? 2024 Elsevier B.V.The Minimum Set Cover Problem (MSCP) is a combinatorial optimization problem belonging to the NP-Hard class in computer science. For this reason, there is no algorithm that in the worst case ensures finding an optimal solution in polynomial-...
The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains greatest number of uncovered elements and adds the selected p sets to partial set cover. The process of adding p sets is repeated until all the elements are covered. When p=1 it ...
Set cover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of approximation ratio of this algorithm. The author improves the approximation ratio 2lnndirectly derived from set cover to 1.14lnnby applying potential function techni...
The SCP is an NP-hard combinatorial optimisation problem. In the case of the Minimum SCP, there exists a polynomial-time approximation algorithm that is guaranteed to return a solution that is worse than the minimum number of sets required to cover A by a factor of at most 1 + logm[Johnso...
0. Raz and Safra [18] proved that if P = N P then for some constant c, the unweighted set cover problem cannot be approximated within a factor c log n. This result shows that the greedy algorithm is an asymptotically best possible approximation algorithm for the weighted and unweighted ...
Set Covering Problem (SCP) is an optimization problem that seeks the smallest set of elements, or sets, to cover a given universe. Implementations of solving SCP involve several techniques: 1. **Greedy Algorithm**: An iterative approach where at each step, the set with the highest coverage-...
If we think 3-SAT is hard (and we do) then set cover must also be hard. So if we can’t hope to solve it exactly we should try to approximate the best solution. The greedy approach The method that Norvig uses in attacking the meta-regex golf problem is the greedy algorithm. The ...
To design our set cover algorithm, we estimate the size of a random greedy maximal matching for an auxiliary multigraph that the algorithm constructs implicitly, without access to its adjacency list or matrix. (在新选项卡中打开) Publication 研究组 Algorithms (Redmond) 研...
Given an instance of the Set Cover with Pairs Problem SCP(G, U, S) as in Definition 1, there exists an efficient (classical) algorithm that computes an instance of the Ising Hamiltonian ground state problem ISING(h, J) with and where the number of qubits involved in the Hamiltonian is ...
Fürer, M., Yu, H.: Packing-based approximating algorithm for the k-set cover problem, http://arxiv.org/abs/1109.3418 Goldschmidt, O., Hochbaum, D.S., Yu, G.: A modified greedy heuristic for the set covering problem with improved worst case bound. Information Processing Letters 48,...