The Graph Coloring Problem: A Bibliographic Survey

Pardalos, Pãnos M.; Mavridou, Thelma D.; Xue, Jue

doi:10.1007/978-1-4613-0303-9_16

Cited by 72 publications

(52 citation statements)

References 344 publications

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“…Even the problem of finding an approximation to the chromatic number of a graph is difficult. It has been shown that if there were an algorithm with polynomial worst-case time complexity that could approximate the chromatic number of a graph up to a factor of 2, then there would also exist an algorithm with polynomial worst-case time complexity for finding the chromatic number of the graph (Pardalos, Mavridou, Xue, 1998, Feige, Kilian, 998, Håstad, 1999, Khot, 2001, Zuckerman, 2007, Lewis, 2015.…”

Section: Graph Coloringmentioning

confidence: 99%

Efficient Course and Exam Scheduling Using Graph Coloring

Papaioannou¹,

Athanassopoulos²,

Kaklamanis³

2017

IJAEDU- International E-Journal of Advances in Education

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Graphs are discrete structures composed of vertices and edges connecting these vertices. Graphs are used in almost all disciplines as abstract models for the representation and study of a wide range of relations and processes in physical, biological, social and information systems. Many practical problems in a variety of areas like computer and communication networks, social networks, transportation networks, cellular networks, linguistics, chemistry, physics, biology can be represented and studied by graphs.Real-world entities -like molecules, persons, groups, roles, species, computing and communication devices, terms -correspond to vertices. Relations among such entities -like preference, domination, independence, interference, proximity, constraints -imply the existence of edges between corresponding vertices. Thus, focusing on the abstract graph model instead of studying each particular instance as a different real-world problem reveals common underlying properties, deficiencies and principles. In this way, efficient approaches to real-world problems emerge from the theoretical study of their abstractions.In this work, we use graph coloring to propose efficient solutions to scheduling problems arising in higher education. The objective of the graph coloring problem is to assign colors to graph vertices so that adjacent vertices, i.e., vertices connected by an edge, receive different colors. We consider as the objective of scheduling problems in higher education, like lecture and exam scheduling, to assign time/day slots to teaching or examination activities so that the maximum number of students can attend them with the fewest possible conflicts.Our main motivation has been the crucial issue of efficient course and exam schedules often arising in departments of the University of Patras, Greece. Students usually have to attend lectures or exams scheduled in overlapping or simultaneous time slots. However, course and exam schedules are created based on heuristic approaches which may work well on average but certainly leave several room for improvement.What if a graph-theoretic approach were used? Courses correspond to vertices of a graph and there is an edge between two vertices if and only if an appropriately selected minimum population of students attends corresponding courses (lectures/exams). Then, a coloring of such an underlying graph suggests an appropriate schedule for teaching/examination activities.Using a simple coloring algorithm and the MATLAB programming environment, we have designed and developed a scheduling application which receives as input courses and constraints and outputs an efficient lecture/examination schedule. Experimental evaluation suggests that our application works well in practice. Ongoing work focuses on the use of a more involved coloring algorithm for addressing more complex course scheduling instances while minimizing required time resources.

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Section: Graph Coloringmentioning

confidence: 99%

Efficient Course and Exam Scheduling Using Graph Coloring

Papaioannou¹,

Athanassopoulos²,

Kaklamanis³

2017

IJAEDU- International E-Journal of Advances in Education

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“…Moreover, also several population-based and hybrid algorithms have been proposed [16,28,45]. For a survey on different heuristics, we refer to [35], [29] and [26].…”

Section: The Graph Coloring Problemmentioning

confidence: 99%

Algorithm Selection for the Graph Coloring Problem

Musliu

Schwengerer

2013

Lecture Notes in Computer Science

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Abstract. 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 highest expected performance. To achieve better performance for the machine learning algorithms, we investigate the impact of parameters, and evaluate different data discretization and feature selection methods. Finally, we evaluate our approach, which exploits the existing GCP techniques and the automated algorithm selection, and compare it with existing heuristic algorithms. Experimental results show that the GCP solver based on machine learning outperforms previous methods on benchmark instances.

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“…This combinatorial optimization problem is known as the minimum coloring problem. A survey on minimum coloring problems can, for example, be found in Randerath and Schiermeyer (2004) and Pardalos et al (1999). An application of the minimum coloring problem is, for example, scheduling courses at secondary schools, where some courses are compulsory and other courses are electives.…”

Section: Introductionmentioning

confidence: 99%

Simple and three-valued simple minimum coloring games

2016

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In this paper minimum coloring games are considered. We characterize the class of conflict graphs inducing simple or three-valued simple minimum coloring games. We provide an upper bound on the number of maximum cliques of conflict graphs inducing such games. Moreover, a characterization of the core is provided in terms of the underlying conflict graph. In particular, in case of a perfect conflict graph the core of an induced three-valued simple minimum coloring game equals the vital core.

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The Graph Coloring Problem: A Bibliographic Survey

Cited by 72 publications

References 344 publications

Efficient Course and Exam Scheduling Using Graph Coloring

Efficient Course and Exam Scheduling Using Graph Coloring

Algorithm Selection for the Graph Coloring Problem

Simple and three-valued simple minimum coloring games

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