In this paper, the tile assembly model can be applied to solve the set cover problem which is a well-known NP-complete problem. In order to achieve this, we design a MinSetCover system which is composed of three parts, the initial configuration subsystem, the nondeterministic choosing ...
be hard and, roughly speaking, by reducing it to set cover we include set cover in a class called NP-complete, and if any one of these problems can be solved efficiently, then they all can (this is the famous P versus NP problem, and an efficient algorithm would imply P equals NP)....
SCP is NP-complete most simply because Set Cover (SC) is a special case of SCP56 and a solution to SCP is clearly efficiently verifiable. Since SC is NP-complete itself, any SCP instance can be rewritten as an instance of SC with polynomial overhead. The Ising Hamiltonian construction for...
Set covering is a classical problem in combinatorial optimization and computer science, which was proved to be NP-complete in [1] in 1972. Given a set V and a family of its subsets U, the classical set covering problem is to find a subfamily S⊆U with the minimum cardinality, satisfying...
1.Define SET COV ER to be {(U,S 1,...,S m ,k )|∀i ,S i ⊂U ,and there is I ⊆{1,...,m }with |I |=k and U = i ∈I {S i }Show that SET COV ER is NP -complete.[20points]Solution:SET-COVER can be seen as a generalization of VERTEX COVER.For a ...
Hitting Set问题在生物计算等领域有着重要的应用.在引入参数计算和复杂性理论后,Set Cover和Hitting Set问题再次成为研究的热点.首先介绍Set Cover和Hitting Set的各种分类问题及其定义,并对各种分类问题的计算复杂性和相关算法的研究进展加以分析总结,给出(k,h)-Set Cover和(k,d)-Set Cover问题的复杂性证明.最后...
Since SC is NP-complete itself, any SCP instance can be rewritten as an instance of SC with polynomial overhead. The Ising Hamiltonian construction for Set Cover is explicitly known39,50. Hence it is natural to consider using the chain of reductions from SCP to SC and then from SC to ...
Show thatHITTING SETisNP-complete. Solution 首先,HITTING SET是一个NP问题。 对于H中的所有元素,和Si逐个比较是否有交集并且大小小于等于b,这个操作显然是多项式时间复杂度的问题。 其次,Vertex Cover是一个NP难问题。 由书本P241、242,可知最小顶点覆盖问题(Vertex Cover)是NP难问题。
The minimum set cover problem is a classical NP-complete problem in computer science. In this paper, the algorithmic tile self-assembly model is used to implement the minimum set cover problem by executing four operations: nondeterministic guess operation, AND operation, copy operation and the ...
Once a complete cover C is constructed, redundant columns, that is, columns that only cover rows that are also covered by other columns in C, are eliminated. This is done by the procedure removeRedundantColumns, which examines the columns of the solution in non-increasing order of their cost...