Abstract

Throughout the study of various theories of algorithms much work has been done in the area of traversal and solving optimization problems on graphs. Some of this work includes studies of finding the Minimal-Cost Spanning Trees (MST) in directed and undirected connected graphs. Several algorithms have been developed for such task. These algorithms tend to differ in performance based on various factors, such as graph density, size of problem spaces, range of weights that can be assigned to the edges of the graphs, edge weight distributions, etc. The data structures used by an algorithm can have a significant impact on algorithm's performance, for each of the aforementioned factors. This thesis presents the results of the experimental study of the impact the data structures have on performances of Kruskal's and Prim's algorithms for finding Minimum-Cost Spanning Trees in connected undirected graphs. The goal of this study is to compare performance of the practical implementations of Kruskal's and Prim's algorithms to their theoretical counterparts, as well as to measure and compare the differences in performances for various implementations of one algorithm, with respect to different implementation of the essential data structures. Performances of different algorithms are studied with respect to each-other for several variations of the types of data. As a result, a table depicting a schedule for use of the various implementations of either of the algorithms, as related to the type of graph used, is presented. The algorithms are implemented and executed on a single Sun UltraSparc workstation, in order to eliminate the discrepancies, which may result from the differences in the processor speeds and variable CPU loads on multiple test machines. The following implementations are studied: Kruskal's Algorithm with heapsort, and disjoint-sets using union-by-rank and path-compression heuristic Kruskal's Algorithm with counting sort and disjoint-sets using union-by-rank and path-compression heuristic Prim's Algorithm with brute force implementation of priority queues Prim's Algorithm with priority queue implemented using a proper implementation of binary heap with "bubble-up" performed each time a decrease-key operation is performed for a vertex Prim's Algorithm with priority queue implemented using a "lazy" implementation of binary heap with "bubble-up" performed after all decrease-key operations are performed for a vertex Prim's Algorithm with priority queue implemented using a binomial heap Prim's Algorithm with priority queue implemented using a Fibonacci heap Upon the conclusion of the experiment, the best results were obtained from the implementation of Prim's algorithm using the "lazy" heap implementation of a priority queue. For sparse graphs, Kruskal's algorithm with counting sort performed very well, while for higher density graphs, Prim's algorithm with binomial heap performed very well.

Library of Congress Subject Headings

Trees (Graph theory); Algorithms

Publication Date

1998

Document Type

Thesis

Department, Program, or Center

Computer Science (GCCIS)

Advisor

Radziszowski, Stanislaw

Advisor/Committee Member

Anderson, Peter

Advisor/Committee Member

Niemi, Rayno

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA166.2 .B47 1998

Campus

RIT – Main Campus

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