Jodi Wineman

Date of Award


Document Type


Degree Name

Master of Arts (MA)



First Advisor

Dr. Hesham H. Ali


Scheduling is a classical field with many challenging problems and interesting results. A scheduling problem emerges wherever there is a choice as to the order in which a number of tasks can be performed and/or the assignment of the tasks to the available resources for processing . In this thesis, we focus on a version of the scheduling problem that deals with scheduling precedence constrained tasks onto the multi processors of a given distributed system with the goal of minimizing the schedule time. This scheduling problem has been proven to be NP-hard even when several restrictions are applied. This implies that an optimal and efficient solution for solving the problem is not likely to exist. Therefore, researchers in this field have been focusing their attention on solving very special versions of the problem or developing fast heuristics for solving the problem in general. In this work, we propose a new approach for developing a scheduling heuristic that is based on a theoretical foundation. Since precedence constrained tasks can be modeled by a partially ordered set, known results from the field of partial orders can be used to solve the scheduling problem. In particular, we look into another scheduling problem, known as the jump number problem in partially ordered sets, to provide a helpful tool in developing a new scheduling heuristic. Given a partially ordered set there exist several efficient, and optimal, algorithms for finding a linear extension of the tasks with the maximum number of unrelated consecutive tasks. Since the order of tasks in such a linear extension explore the independence relations among the tasks, we propose to use this order in a priority-based scheduling algorithm. We then study the relationship between the characteristic of the linear extension and the length of the scheduling algorithm and one of the frequently used algorithms will be conducted. Randomly generated partial orders that represent precedence constrained tasks will be used to test the developed algorithms and measure their performance.


A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree Master of Arts University of Nebraska at Omaha. Copyright 1999 Jodi Wineman

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