A Performance Comparison of Graph Coloring Algorithms

Yıl 2016, Cilt: 4 Sayı: Special Issue-1, 1 - 7, 15.12.2016

Murat Aslan , Nurdan Akhan Baykan

https://doi.org/10.18201/ijisae.273053

Cited By: 20

Öz

Graph coloring problem (GCP) is getting more popular to solve the
problem of coloring the adjacent regions in a map with minimum different number
of colors. It is used to solve a variety of real-world problems like map
coloring, timetabling and scheduling. Graph coloring is associated with two
types of coloring as vertex and edge coloring. The goal of the both types of
coloring is to color the whole graph without conflicts. Therefore, adjacent
vertices or adjacent edges must be colored with different colors.  The number of the least possible colors to be
used for GCP is called chromatic number. As the number of vertices or edges in
a graph increases, the complexity of the problem also increases. Because of
this, each algorithm can not find the chromatic number of the problems and may
also be different in their executing times. Due to these constructions, GCP is
known an NP-hard problem. Various heuristic and metaheuristic methods have been
developed in order to solve the GCP. In this study, we described First Fit
(FF), Largest Degree Ordering (LDO), Welsh and Powell (WP), Incidence Degree
Ordering (IDO), Degree of Saturation (DSATUR) and Recursive Largest First (RLF)
algorithms which have been proposed in the literature for the vertex coloring
problem and these algorithms were tested on benchmark graphs provided by
DIMACS. The performances of the algorithms were compared as their solution
qualities and executing times. Experimental results show that while RLF and
DSATUR algorithms are sufficient for the GCP, FF algorithm is generally
deficient. WP algorithm finds out the best solution in the shortest time on
Register Allocation, CAR, Mycielski, Stanford Miles, Book and Game graphs. On
the other hand, RLF algorithm is quite better than the other algorithms on Leighton,
Flat, Random (DSJC) and Stanford Queen graphs.

Anahtar Kelimeler

Chromatic number, Graph coloring algorithms

Kaynakça

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