Algorithm For Graph Coloring Problem Research Articles

A Comparative Study of Cat Swarm Algorithm for Graph Coloring Problem: Convergence Analysis and Performance Evaluation

The Graph Coloring Problem (GCP) is a significant optimization challenge widely suitable to solve scheduling problems. Its goal is to specify the minimum colors (k) required to color a graph properly. Due to its NP-completeness, exact algorithms become impractical for graphs exceeding 100 vertices. As a result, approximation algorithms have gained prominence for tackling large-scale instances. In this context, the Cat Swarm algorithm, a novel population-based metaheuristic in the domain of swarm intelligence, has demonstrated promising convergence properties compared to other population-based algorithms. This research focuses on designing and implementing the Cat Swarm algorithm to address the GCP. By conducting a comparative study with established algorithms, our investigation revolves around quantifying the minimum value of k required by the Cat Swarm algorithm for each graph instance. The evaluation metrics include the algorithm's running time in seconds, success rate, and the mean count of iterations or assessments required to reach a goal.

Exponential-Time Quantum Algorithms for Graph Coloring Problems

The fastest known classical algorithm deciding the k-colorability of n-vertex graph requires running time varOmega (2^n) for kge 5. In this work, we present an exponential-space quantum algorithm computing the chromatic number with running time O(1.9140^n) using quantum random access memory (QRAM). Our approach is based on Ambainis et al’s quantum dynamic programming with applications of Grover’s search to branching algorithms. We also present a polynomial-space quantum algorithm not using QRAM for the graph 20-coloring problem with running time O(1.9575^n). For the polynomial-space quantum algorithm, we essentially develop (4-epsilon )^n-time classical algorithms that can be improved quadratically by Grover’s search.

A Linked List-Based Exact Algorithm for Graph Coloring Problem

A Linked List-Based Exact Algorithm for Graph Coloring Problem

A Binary Cuckoo Search Algorithm for Graph Coloring Problem

The Graph Coloring Problem (GCP) is one of the most interesting, studied, and difficult combinatorial optimization problems. That is why several approaches were developed for solving this problem, including exact approaches, heuristic approaches, metaheuristics, and hybrid approaches. This paper tries to solve the graph coloring problem using a discrete binary version of cuckoo search algorithm. To show the feasibility and the effectiveness of the algorithm, it has used the standard DIMACS benchmark, and the obtained results are very encouraging.

Hybrid Discrete Particle Swarm Algorithm for Graph Coloring Problem

Graph coloring problem (GCP) is one of the most studied combinatorial optimization problems. It is important in theory and practice. There have been many algorithms for graph coloring problem, including exact algorithms and (meta-)heuristic algorithms. In this paper, we attempt another meta-heuristic method ¾ particle swarm optimization to graph coloring problem. Particle swarm optimization (PSO) was originally developed for continuous problem. To apply PSO to discrete problem, the standard arithmetic operators of PSO are required to be redefined over discrete space. A conception of distance over discrete solution space is introduced. Under this notion of distance, the PSO operators are redefined. After reinterpreting the composition of velocity of a particle, a general discrete PSO algorithm is proposed. In order to solve graph coloring problem by the discrete PSO algorithm, an algorithm to implement the crucial PSO operator ¾ difference of two positions (solutions) is design ed . Then, a hybrid discrete PSO algorithm for graph coloring problem is propose d by combining a local search. Empirical study of the proposed hybrid algorithm is also carried out based on the second DIMACS challenge benchmarks. The experimental results are competitive with that of other well-known algorithms .