An instance ( C , U ) of the set-cover problem is k -bounded if the number of occurrences in C of any element is bounded by a constant k 2. We present an approximation algorithm for the k -bounded set-cover problem, that achieves the ratio k k(k1) 1ε k +o(1) , where ε ...
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...
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The unweighted k-set cover prob- lem is known to be NP-complete [13] and MAX SNP-hard for all k ≥ 3 [3, 14, 16]. Another algorithm for the weighted set cover problem by Hochbaum [10] has an approximation ratio that depends on the maximum number of subsets that contain any given...
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution...
While the constructive phase uses a procedure in consonance with the procedures to solve the set cover- ing problem, the local search phase is completely based on the constraint satisfiability problem. During local search phases, the solution may therefore be no longer feasible for the original ...
27 September 2016 Yudong Cao1, Shuxian Jiang1, Debbie Perouli2 & Sabre Kais3,4 Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry...
Set cover is what’s called NP-hard, and one implication is that we shouldn’t hope to find an efficient algorithm that will always give you the shortest regex for every regex golf problem. But despite this, there are approximation algorithms for set cover. What I mean by this is that ...
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-...