4

4

6448

Anti-Homomorphism in Fuzzy Ideals

The anti-homomorphic image of fuzzy ideals, fuzzy
ideals of near-rings and anti ideals are discussed in this note. A
necessary and sufficient condition has been established for near-ring
anti ideal to be characteristic.

Fuzzy Ideals, Anti fuzzy subgroup, Anti fuzzy ideals, Anti homomorphism, Lower α level cut.

3

11182

An Effective Algorithm for Minimum Weighted Vertex Cover Problem

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

2

12153

Approximating Maximum Weighted Independent Set Using Vertex Support

The Maximum Weighted Independent Set (MWIS)
problem is a classic graph optimization NP-hard problem. Given an
undirected graph G = (V, E) and weighting function defined on the
vertex set, the MWIS problem is to find a vertex set S V whose total
weight is maximum subject to no two vertices in S are adjacent. This
paper presents a novel approach to approximate the MWIS of a graph
using minimum weighted vertex cover of the graph. Computational
experiments are designed and conducted to study the performance
of our proposed algorithm. Extensive simulation results show that
the proposed algorithm can yield better solutions than other existing
algorithms found in the literature for solving the MWIS.

weighted independent set, vertex cover, vertex support,heuristic, NP - hard problem.

1

12686

Optimization of Unweighted Minimum Vertex Cover

The Minimum Vertex Cover (MVC) problem is a classic
graph optimization NP - complete problem. In this paper a competent
algorithm, called Vertex Support Algorithm (VSA), is designed to
find the smallest vertex cover of a graph. The VSA is tested on a
large number of random graphs and DIMACS benchmark graphs.
Comparative study of this algorithm with the other existing methods
has been carried out. Extensive simulation results show that the VSA
can yield better solutions than other existing algorithms found in the
literature for solving the minimum vertex cover problem.

vertex cover, vertex support, approximation algorithms,NP - complete problem.