Vertex cover problem has a numerous real life applications such as communications, bioinformatics, engineering, statics, and mathematics to study and process biological data. NP complete problems are unlikely to find a polynomial-time algorithm for solving vertex-cover problem accurately because they ...
(mn2), where in the case of solving the problem of minimal vertex cover of arbitrary graphs n is the number of vertices in the graph, m is the number of edges in the graph, and in the case of solving the problem of minimal cover n is the number of columns in the Boolean matrix, ...
We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in \\(({\\it \\Delta}+1)^2\\) synchronous communication rounds, where \\({\\it \\Delta}\\) is the maximum degree of the graph. For \\({\\it \\De...
It is found that there exists a phase transition at the critical average degree e/(α-1), below which a replica symmetric ansatz in the replica method holds and the algorithm estimates exactly the same solution of the problem as that by the replica method. In contrast, above the critical ...
As it is NP complete problem, we can have an approximate time algorithm to solve the vertex cover problem. We will modify the algorithm to have an algorithm which can be solved in polynomial time and which will give near to optimum solution. It is a simple algorithm which will be based ...
[2004]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big well-separated sets in the sense of Arora et al. [2004] ...
Maximum Minimal Vertex Cover Parameterized by Vertex Cover Summary: The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms paramet......
I've been recently dealing with the classical problem of finding the minimum vertex cover in a bipartite graph. The common approach is to set direction to all edges and run DFS from all vertices of the left part outside of the matching. However, this solution seems too clever for me. A...
The minimum generalized vertex cover problem Let G = (V, E) be an undirected graph, with three numbers d0(e) ≥ d1(e) ≥ d2(e) ≥ 0 for each edge e ∈ E. A solution is a sub... R Hassin,A Levin - 《Acm Transactions on Algorithms》 被引量: 47发表: 2006年 Minimum vertex...
Let kappa(G) be the smallest number of chips needed to cover all vertices of G. We prove that kappa(G) is equal to the minimum cardinality of a vertex cover of G^2. Moreover, we show that the initial distribution of chips is given by a solution of the vertex cover problem....