Random-Tree Diameter and the DiameterConstrained MST

Random-Tree Diameter and the DiameterConstrained MST (2000)

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by Ayman Abdalla , Narsingh Deo , Pankaj Gupta

Venue:	MST,” Congressus Numerantium
Citations:	8 - 1 self

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Datum	Value	Source
TITLE	Random-Tree Diameter and the DiameterConstrained MST	user correction - Legacy Corrections
AUTHOR NAME	Ayman Abdalla	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Computer Science; University of Central Florida	SVM HeaderParse 0.2
AUTHOR NAME	Narsingh Deo	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Computer Science; University of Central Florida	SVM HeaderParse 0.2
AUTHOR NAME	Pankaj Gupta	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Computer Science; University of Central Florida	SVM HeaderParse 0.2
ABSTRACT	A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. Understanding the behavior of tree diameter is useful, for example, in determining an upper bound on the expected number of links between two arbitrary documents on the World Wide Web. The DiameterConstrained MST (DCMST) problem can be stated as follows: given an undirected, edge-weighted graph G with n nodes and a positive integer k, find a spanning tree with the smallest weight among all spanning trees of G which contain no path with more than k edges. This problem is known to be NP-complete, for all values of k; 4 k #n - 2). In this paper, we investigate the behavior of the diameter of MST in randomly-weighted complete graphs (in Erds-Rnyi sense) and explore heuristics for the DCMST problem. For the case when the diameter bound k is small---independent of n, we present a one-time-tree-construction (OTTC) algorithm. It constructs a DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to the tree at each stage of the tree construction. This algorithm is fast and easily parallelizable. We also present a second algorithm that outperforms OTTC for larger values of k. It starts by generating an unconstrained MST and iteratively refines it by replacing edges, one by one, in the middle of long paths in the spanning tree until there is no path left with more than k edges. As expected, the performance of this heuristic is determined by the diameter of the unconstrained MST in the given graph. We discuss convergence, relative merits, and implementation of t...	user correction - Legacy Corrections
YEAR	2000	INFERENCE
VENUE	MST,” Congressus Numerantium	INFERENCE
VENUE TYPE	TECHREPORT	INFERENCE
PAGES	161--182	INFERENCE
VOLUME	144	INFERENCE
TECH	Technical Report CS-TR-00-02	INFERENCE
CITATIONS	21 found	ParsCit 1.0