Keywords
Algorithms; Graph theory; Trees (Graph theory)
Abstract
In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameter-constrained minimum spanning tree (DCMST) of a given undirected, edge-weighted graph, G, is the smallest-weight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NP-complete for all values of k; 4 ≤ k ≤ (n - 2), except when all edge-weights are identical.
A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a data-structure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space.
We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomial-time algorithms for an approximate DCMST. One of our new algorithms constructs approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present ab algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter-4 tree is also used for evaluating the quality of other algorithms. All five algorithms were implemented on a PC, and four of them were also parallelized and implemented on a massively parallel machine-the MasPar MP-1. We discuss convergence, relative merits, and implementation of these heuristics. Our extensive empirical study shows that the heuristics produce good solutions for a wide variety of inputs.
Graduation Date
2001
Advisor
Deo, Narsingh
Degree
Doctor of Philosophy (Ph.D.)
College
College of Engineering and Computer Science
Department
Electrical Engineering and Computer Science
Degree Program
Electrical Engineering and Computer Science
Format
Language
English
Rights
Written permission granted by copyright holder to the University of Central Florida Libraries to digitize and distribute for nonprofit, educational purposes.
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
Identifier
DP0002215
Subjects
Dissertations, Academic -- Engineering; Engineering -- Dissertations, Academic
STARS Citation
Abdalla, Ayman Mahmoud, "Computing a Diameter-constrained Minimum Spanning Tree" (2001). Retrospective Theses and Dissertations. 1085.
https://stars.library.ucf.edu/rtd/1085
Contributor (Linked data)
Deo, Narsingh, 1936- [VIAF]
Deo, Narsingh, 1936- [LC]
University of Central Florida. College of Engineering and Computer Science (Q7895235)
University of Central Florida. College of Engineering and Computer Science [VIAF]
University of Central Florida. College of Engineering and Computer Science [LC]
Accessibility Status
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