Approximation Algorithms for Vertex Happiness

Approximation Algorithms 1.1 Minimum Vertex Cover

1 Approximation Algorithms Any known algorithm that finds the solution to an NP-hard optimization problem has exponential running time. However, sometimes polynomial time algorithms exist which find a " good " solution instead of an optimum solution. Given a minimization problem and an approximation algorithm, we can evaluate the algorithm as follows. First, we find a lower bound on the optimum...

Approximation Algorithms for Edge Partitioned Vertex Cover Problems

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a cost function c : V → Z, a partition P1, . . . , Pr of the edge set E, and a parameter ki for each partition Pi. The goal is to find a minimum cost set of vertices which cover at least ki edges from the partition Pi. We call this the Partition-VC problem. In this paper, we...

On Some Approximation Algorithms for Dense Vertex Cover Problem

In this work we study the performance of some algorithms approximating the vertex cover problem (VCP) with respect to density constraints. We consider a modiication of the algorithm of Karpinski and Zelikovsky 9] for the weighted VCP and prove a performance guarantee for this algorithm in terms of a new density parameter. Also we investigate the hardness of approximation for the VCP on everywhe...

Constant Approximation Algorithms for Guarding Simple Polygons using Vertex Guards

The art gallery problem enquires about the least number of guards sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. Most standard versions of this problem are known to be NP-hard. In 1987, Ghosh provided a deterministic O(log n)approximation algorithm for the case of vertex guards and edge guards in simple polygons. In the same paper, Ghosh also conjecture...

Improved Approximation Algorithms for the Partial Vertex Cover Problem