Research Article

Year 2017,
Volume: 3 Issue: 7, 51 - 59, 30.04.2017
### Abstract

### Keywords

### References

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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Year 2017,
Volume: 3 Issue: 7, 51 - 59, 30.04.2017
### Abstract

### References

There are 1 citations in total.

Journal Section | Articles |
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Authors | |

Publication Date | April 30, 2017 |

Submission Date | April 30, 2017 |

Published in Issue | Year 2017Volume: 3 Issue: 7 |

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