We present an automated algorithm selection method based on machine learning for the graph coloring problem (GCP). For this purpose, we identify 78 features for this problem and evaluate the performance of six state-of-the-art (meta)heuristics for the GCP. We use the obtained data to train several classification algorithms that are applied to predict on a new instance the algorithm with the hig...

The graph-theoretic parameter that has probably received the most attention over the years is the chromatic number. As is well-known, the coloring problem is an NP-Complete problem. In this paper, it has been solved by means of molecular biology techniques. The algorithm is highly parallel and has satisfactory fidelity. This work shows further evidence for the ability of DNA computing to solve ...

In this chapter a new formulation of the robust graph coloring problem (RGCP) is proposed. In opposition to classical GCP defined for the given graph G(V,E) not only elements of E but also Ē can be subject of color conflicts in edge vertices. Conflicts in Ē are assigned penalties 0<P(e)<1. In addition to satisfying constraints related to the number of colors and/or a threshold of the acceptable...

Graph coloring has numerous applications and is a wellknown NP-complete problem. The goal of this paper is to survey recent results of the authors on coloring and improper coloring of sparse graphs and to point out some polynomial-time algorithms for coloring (not necessarily optimal) of graphs with bounded maximum average degree. Mathematics Subject Classification: 05C15, 05C35

Recent advances in computer vision, information retrieval, and molecular biology amply demonstrate the value and importance of graph matching. However, graph matching algorithms developed to date are either application domainspecific or severely limited by the problem size. This paper presents a unified solution for the broad range of major graph matching problems. Particularly, the new algorit...

The max-edge-coloring problem (MECP) is finding an edge colorings {E1, E2, E3, ..., Ez} of a weighted graph G=(V, E) to minimize { } ∑ = ∈ z i i k k E e e w 1 ) ( max , where w(ek) is the weight of ek. In the work, we discuss the complexity issues on the new graph problem and its variants. Specifically, we design a 2-approximmation algorithm for the max-edge-coloring problem on biplanar graphs....

In the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NPcomplete within a broad spectrum of graph parameters. This affects the complexity of batch scheduling of unit-length jobs with cubic incompatibility graph on three uniform proces...

A squarefree word is a sequence w of symbols such that there are no strings x, y, and z for which w = xyyz. A nonrepetitive coloring of a graph is an edge coloring in which the sequence of colors along any open path is squarefree. We show that determining whether a graph G has a nonrepetitive k-coloring is Σ p 2 -complete. When we restrict to paths of lengths at most n, the problem becomes NP-c...

Graph coloring is a well known problem from graph theory that, when solving it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k, one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local...

We consider two generalizations of the edge coloring problem in bipartite graphs. The first problem we consider is the weighted bipartite edge coloring problem where we are given an edge-weighted bipartite graph G = (V, E) with weights w : E → [0, 1]. The task is to find a proper weighted coloring of the edges with as few colors as possible. An edge coloring of the weighted graph is called a pr...