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This paper presents a graphcoloringbased algorithm for the exam scheduling application, with the objective of achieving fairness, accuracy, and optimal exam time period. Through the work, we consider few assumptions and constraints, closely related to the general exam scheduling problem, and mainly driven from accumulated experience at various collages. The performance of the algorithm is also a major concern of this paper.



An undirected graph G is an ordered pair V, E where V is a set of nodes and E is a set of nondirected edges between nodes. Two nodes are said to be adjacent if there is an edge between them. The graph coloring is a wellknown problem. Node coloring assigns colors to the nodes of the graph such that no two adjacent nodes have the same color. Edge coloring assigns colors to the edges of the graph such that no two adjacent edges have the same color. Two edges are said to be adjacent if they both share a node in common. General graph coloring algorithms are well known and have been extensively studied by researchers.

Exam scheduling is a challenging task that universities and colleges face several times every year.

The challenge is to schedule so many exams of courses in a limited, and usually short, period of time. An Exam schedule should avoid conflicts, in the sense that no two or more exams for the same student are scheduled at the same time. Part of the challenge is to achieve fairness for the students. A fair schedule does not schedule more than two exams, for example for a student on one day. In the meantime, a fair schedule does not leave a big gap between exams for the students. The exam scheduling problem is defined as follows: We first represent the courses by nodes of a graph, where two nodes are adjacent if the two corresponding courses are registered by at least one student. Then, it is required to assign each course represented by a node a time slot, such that no two adjacent nodes have the same slot, in condition that a set of constraints imposed on the problem are also met. We solve this problem by using node graph coloring technique.

This study provides a mechanism for automatic examschedule generation that achieves fairness, and minimizes the exam period. As a result, this paper presents a graphcoloringbased algorithm for the exam scheduling application which achieves the objectives of fairness, accuracy, and optimal exam time period.

Numerous studies have considered the problem of exam scheduling. The main difference between various studies is the set of assumptions and constraints taken into consideration. Burke, Elliman and Weare, for example, followed a similar approach using graph coloring. However, in their algorithm, they addressed only the conflicts without any constraints. Moreover, the algorithm presented in does not eliminate conflicts, and only aims at minimizing conflicts. In this paper, we consider few but important assumptions and constraints, closely related to the general exam scheduling, and mainly driven from the real life requirements collected through the experience at various universities. Such assumptions and constraints are distinct from those present in more general graph coloring problems. We summarize the main assumptions and constraints as follows:

1.The number of exam periods per day Time Slots TS can be set by the user. TS depend on college/department specific constraints. For example, a university that uses a 2hours exam period and begins the exam day at 8:00 am and finish at 8:00 pm, may set TS to 5.

2.The number of concurrent exam sessions or concurrency level Np depends on the number of available halls, and the availability of faculty to conduct the exams. Np is determined by the registrars office. This paper assumes that Np is a system parameter and the scheduling algorithm has been examined with several Np values.

3.A student shall not have more than y exams per day fairness requirement, and is treated as a system tunable parameter.

4.A student shall not have a gap of more than x days between two successive exams, and this factor is to be determined by the college or department another fairness requirement.

5.The schedule shall be done in the minimal possible period of time, i.e., minimize the number of exam slots and/or number of exam days. The exam time period is an outcome of the scheduling algorithm.


The current system at the collage, the collage only considers the hard constraints and ignores the soft constraints. For example, if the duration for the exam is seven days, the system will make sure the entire exam involve will be spread out within that duration without checking the resources allocation and student constraints. There are no standards for solution qualities that measure either the exam timetable is feasible or not. The system analyst just makes sure that there is no clashing for the students but get heavy work load on the student like a student writing a course of 6 credit unit on concurrent time without a rest of mind and soul.

Furthermore, each day there are only two slots available which are morning session and afternoon session. The main objective of an exam timetable is to guarantee that all exams are scheduled and students can sit all the exams that they are required to do and no string attaches.


This study is primarily aimed at increasing efficiency in operations, reducing error and running cost, stabilising the degree of equatorial point of and standard level of exam schedule and runs the distribution of exam time in the collage by introducing an automated exam time scheduling system using color grapy algorithm system.


The purpose of this study is to improve current operational process in the collage in scheduling exam timetable to avoid classing by developing efficient computer software that can handle time schedule in a computerized fashion.

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