**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4

# Search results for: NP-complete problem

##### 4 Using A Hybrid Algorithm to Improve the Quality of Services in Multicast Routing Problem

**Authors:**
Mohammad Reza Karami Nejad

**Abstract:**

A hybrid learning automata-genetic algorithm (HLGA) is proposed to solve QoS routing optimization problem of next generation networks. The algorithm complements the advantages of the learning Automato Algorithm(LA) and Genetic Algorithm(GA). It firstly uses the good global search capability of LA to generate initial population needed by GA, then it uses GA to improve the Quality of Service(QoS) and acquiring the optimization tree through new algorithms for crossover and mutation operators which are an NP-Complete problem. In the proposed algorithm, the connectivity matrix of edges is used for genotype representation. Some novel heuristics are also proposed for mutation, crossover, and creation of random individuals. We evaluate the performance and efficiency of the proposed HLGA-based algorithm in comparison with other existing heuristic and GA-based algorithms by the result of simulation. Simulation results demonstrate that this paper proposed algorithm not only has the fast calculating speed and high accuracy but also can improve the efficiency in Next Generation Networks QoS routing. The proposed algorithm has overcome all of the previous algorithms in the literature.

**Keywords:**
Routing,
Quality of Service,
Multicaset,
Learning Automata,
Genetic,
Next Generation Networks.

##### 3 An Effective Algorithm for Minimum Weighted Vertex Cover Problem

**Authors:**
S. Balaji,
V. Swaminathan,
K. Kannan

**Abstract:**

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.

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

##### 2 A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes

**Authors:**
Zohreh O. Akbari

**Abstract:**

**Keywords:**
Clique problem,
Deterministic Polynomial-time
Algorithm,
Equality of P and NP Complexity Classes.

##### 1 Enhanced Traveling Salesman Problem Solving by Genetic Algorithm Technique (TSPGA)

**Authors:**
Buthainah Fahran Al-Dulaimi,
Hamza A. Ali

**Abstract:**

The well known NP-complete problem of the Traveling Salesman Problem (TSP) is coded in genetic form. A software system is proposed to determine the optimum route for a Traveling Salesman Problem using Genetic Algorithm technique. The system starts from a matrix of the calculated Euclidean distances between the cities to be visited by the traveling salesman and a randomly chosen city order as the initial population. Then new generations are then created repeatedly until the proper path is reached upon reaching a stopping criterion. This search is guided by a solution evaluation function.

**Keywords:**
Genetic algorithms,
traveling salesman problem solving,
optimization.