A complete algorithm to solve the graph-coloring problem
نویسندگان
چکیده
The Graph k-Colorability Problem (GCP) is a well known NP-hard problem which consist in finding the k minimum number of colors to paint the vertices of a graph in such a way that any two vertices joined by an edge have always different colors. Many years ago, Simulated Annealing (SA) was used for graph coloring task obtaining good results; however SA is not a complete algorithm and it not always gets the optimal solution. In this paper GCP is transformed into the Satisfiability Problem and then it is solved using a algorithm that uses the Threshold Accepting algorithm (a variant of SA) and the Davis & Putnam algorithm. The new algorithm is a complete one and so it gets better quality that the classical simulated annealing algorithm.
منابع مشابه
الگوریتم ژنتیک با جهش آشوبی هوشمند و ترکیب چندنقطهای مکاشفهای برای حل مسئله رنگآمیزی گراف
Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices have the same color. Graph coloring problem (GCP) is about finding the smallest number of colors needed to color a given graph. The smallest number of colors needed to color a graph G, is called its chromatic number. GCP is a well-known NP-hard problems and, therefore, heuristic algorithms are usually...
متن کاملA practical algorithm for [r, s, t]-coloring of graph
Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring an...
متن کاملSolving a nurse rostering problem considering nurses preferences by graph theory approach
Nurse Rostering Problem (NRP) or the Nurse Scheduling Problem (NSP) is a complex scheduling problem that affects hospital personnel on a daily basis all over the world and is known to be NP-hard.The problem is to decide which members of a team of nurses should be on duty at any time, during a rostering period of, typically, one month.It is very important to efficiently utilize time and effort, ...
متن کاملParallel Jobs Scheduling with a Specific Due Date: Asemi-definite Relaxation-based Algorithm
This paper considers a different version of the parallel machines scheduling problem in which the parallel jobs simultaneously requirea pre-specifiedjob-dependent number of machines when being processed.This relaxation departs from one of the classic scheduling assumptions. While the analytical conditions can be easily statedfor some simple models, a graph model approach is required when confli...
متن کاملA new Simulated Annealing algorithm for the robust coloring problem
The Robust Coloring Problem (RCP) is a generalization of the well-known Graph Coloring Problem where we seek for a solution that remains valid when extra edges are added. The RCP is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. This problem has been proved as NP-hard and in instances larger than 30 vertices, meta-...
متن کاملJust chromatic exellence in fuzzy graphs
A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...
متن کامل