NP-Complete ProblemApproximation AlgorithmThis paper describes an extremely fast polynomial time algorithm, the Near Optimal Vertex Cover Algorithm (NOVCA) that produces an optimal or near optimal vertex cover for any known undirected graph G (V, E). NOVCA constructs the vertex cover by repeatedly ...
Assuming the Unique Game Conjecture, it is NP-hard to approximate the vertex cover problem in graphs for which a local (Δ+1)-coloring is given as input, within any constant factor better than 2−2/(Δ+1). Proof Consider the graph G of Theorem 12 and let n denote the number of v...
ShowthatPUZZLEisNP-complete.Proof--PleaserefertotheslidesofApril17and19 5Showthatco-NP=P1,pwhere co-NP={L:LNP} P1,p={L:k,alanguageL‟inP s.t.(w,x)L‟}} s.t.L={x:w,|w|=O(|x|k),Proof:
and asks whetherGhas a vertex cover of size at mostk.Vertex Coveris one of the six classic NP-complete problems discussed by Garey and Johnson in their famous work on intractability [26
Our focus. Like the class of interval graphs, the class of permutation graphs admits polynomial-time algorithms for rich family problems which are NP-complete in general. Apart from the already mentioned classical hard problems which are polynomial-time solvable for perfect graphs, there also exist...
The main findings are as follows: Binary CSP parameterized by the vertex cover number is $\mathrm{W}[3]$-complete. More generally, for every positive integer $d$, Binary CSP parameterized by the size of a modulator to a treedepth-d graph is $\mathrm{W}[2d+1]$-complete. This ...
The problem is known to be NP -complete see 13 , since the vertex cover problem can be reduced to it; there exist polynomial time algorithms for particular topologies 6, 15 and 17 . The relevance of this problem arises in several areas. For example, it models the problem of removing ...
This paper proves that the problem of finding connected vertex cover in a 2-connected planar graph ( CVC-2 ) with maximum degree 4 is NP-complete. The motivation for proving this result is to give a shorter and simpler proof of NP-Completeness of TRA-MLC (the Top Right Access point ...
NP-Complete ProblemApproximation AlgorithmThis paper describes an extremely fast polynomial time algorithm, the Near Optimal Vertex Cover Algorithm (NOVCA) that produces an optimal or near optimal vertex cover for any known undirected graph G (V, E). NOVCA constructs the vertex cover by repeat...
This problem is NP-complete and thus was studied from parameterized complexity and approximation algorithms view points. Vertex Cover and its generalizations have been important in developing basic and advanced methods and approaches for parameterized and approximation algorithms. Thus, it was named the ...