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...
The set cover problem plays the same role in approximation algorithms that the maximum matching problem played in exact algorithms — as a problem whose study led to the development of fundamental techniques for the entire field. For our purpose this problem is particularly useful, since it offers...
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Since the set cover problem is a fundamental problem, there is an ongoing research effort to improve this approximation ratio using modifications of the greedy algorithm. The previous best improvement of the greedy algorithm is an \\\(\\\left( H_k-{1\\\over 2}ight)\\\) -approximation...
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...
Let me take maximum coverage problem as an example, which given a set system with a number , we ask what is the largest amount of elements we can cover using sets. Theorem. Greedy covering gives a -approximation to the maximum coverage problem. Proof. Let be the number of elements newly...
Finally, we consider a further generalization of the set cover problem in which we aim at minimizing the sum of some concave function of the part sizes. As an application, we derive an approximation ratio for a Rent-or-Buy set cover problem....
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 ...
VERTEX COVER AND SET COVER