Search results for "Minimum degree spanning tree"
showing 3 items of 3 documents
Almost disjoint spanning trees: relaxing the conditions for completely independent spanning trees
2017
International audience; The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by dening (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one tree. We illustrate how (i, j)-disjoint spanning trees provide some nuances between the existence of disjoint connected dominating sets and completely independent spanning trees. We prove that determining if there exist two (i, j)-disjoint spanning trees in a graph G is NP-comple…
Estimating the length of minimal spanning trees in compression of files
1984
Compression of a formatted file by a minimal spanning tree (MST) is studied. Here the records of the file are considered as the nodes of a weighted undirected graph. Each record pair is connected in the graph and the corresponding arc is weighted by the sum of field lengths of those fields which differ in the two records. The actual compression is made by constructing an MST of the graph and by storing it in an economic way to preserve the information of the file. The length of the MST is a useful measure in the estimation of the power of the compression. In the paper we study upper bounds of this length, especially in the case where the field lengths of the different fields may vary. The u…
New insights into the OCST problem
2009
This paper considers the Euclidean variant of the optimal communciation spanning tree (OCST) problem. Researches have analyzed the structure of the problem and found that high quality solutions prefer edges of low cost. Further, edges pointing to the center of the network are more likely to be included in good solutions. We add to the literature and provide additional insights into the structure of the OCST problem. Therefore, we investigate properies of the whole tree, such as node degrees and the Wiener index. The results reveal that optimal solutions are structured in a star-like manner. There are few nodes with high node degrees, these nodes are located next to the graph's center. The m…