Graph Coloring Problem Based on Learning Automata

Abstract

Abstract-The vertex coloring problem is a well-known classical problem in graph theory in which a color is assigned to each vertex of the graph such that no two adjacent vertices have the same color. The minimum vertex coloring problem is known to be an NP-hard problem in an arbitrary graph, and a host of approximation solutions are available. In this paper, four learning automata-based approximation algorithms are proposed for solving the minimum (vertex) coloring problem. It is shown that by a proper choice of the parameters of the algorithm, the probability of approximating the optimal solution is as close to unity as possible. The last proposed algorithm is compared with some well-known coloring algorithms and the results show the efficiency of the proposed algorithm in terms of the color set size and running time of algorithm.

An efficient cluster-based CDMA/TDMA scheme for wireless mobile ad-hoc networks: A learning automata approach

“…In Akbari Torkestani and Meybodi (in press-a, in press-b, in press-d, 2010), a group of variable action-set learning automata is used to solve the vertex coloring problem, or in Akbari Torkestani and Meybodi (in press-a, in press-b, in press-d, 2010) variable action-set learning automata cooperate to find the virtual backbone of the ad hoc networks. It has been shown in Thathachar and Harita (1987), Akbari Meybodi (2009a and2009b) that a learning automaton with a changing number of actions is absolutely expedient and also e-optimal, when the reinforcement scheme is L RÀ I . Such an automaton has a finite set of n actions, a={a 1 , a 2 , y a n }.…”

“…Such a code assignment problem is similar to the NP-hard vertex coloring problem in which no two neighboring clusters (or node) have the same code (or color). The code assignment algorithm we propose in this paper is a distributed version of the first learning automata-based graph coloring algorithm proposed in Akbari Meybodi (2009a and2009b). LACAA is a fully localized algorithm in which each cluster-head is assigned an interference-free code based only on the local (code assignment) information received from the cluster-head of its neighboring clusters.…”

The Design Of New Learning Automata For Problem Graph Coloring

“…We show this suitability by S(E). In [33], four learning automata-based approximation algorithms are proposed for solving the minimum (vertex) coloring problem.It is shown that by a proper choice of the parameters of the algorithm, the probability of approximating the optimal solution is as close to unity as possible.…”

“…The last proposed algorithm is compared with CHECKCOL [13], GLS [9], ILS [5], TPA [6], AMACOL [1], some well-known coloring algorithms and the results show the efficiency of the algorithm [33] in terms of the color set size and running time of algorithm.Graph coloring problem is widely used in real life applications like computer register allocation, air traffic flow management, timetabling, scheduling, frequency assignment, and light wavelengths assignment inoptical networks. The approximation approaches reported in the literatures can be classified as local search approaches, genetic algorithms, fuzzy-based optimizations, evolutionary algorithms, simulated annealing methods, ant colony-based approaches, Markov chain approaches, and neural network approaches.…”

A Learning Automata-Based Cognitive Radio for Clustered Wireless Ad-Hoc Networks

“…Second, supporting the inter-cluster connections by assigning a code to each cluster (code assignment) so that no two neighboring or hidden clusters have the same code, and third, using an efficient TDMA scheme for channel access scheduling within each cluster. Code assignment problem is very similar to the NP-hard [27] vertex coloring problem [28] in graph theory. Besides the above mentioned TDMA schemes, we compare our proposed model with the TDMA part of the following CDMA/TDMA schemes.…”