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On finding the core of a tree with a specified length

โœ Scribed by Edward Minieka; Niranjani H Patel


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
291 KB
Volume
4
Category
Article
ISSN
0196-6774

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A core of a graph G is a path P in G that is central with respect to the property to path P. This paper presents efficient algorithms for finding a core of a tree with ลฝ . a specified length. The sequential algorithm runs in O n log n time, where n is the ลฝ 2 . ลฝ. size of the tree. The parallel alg

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We investigate Prim's standard ''tree-growing'' method for finding a minimum spanning tree, when applied to a network in which all degrees are about d and the edges e ลฝ . have independent identically distributed random weights w e . We find that when the kth ' ลฝ . edge e is added to the current tree

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Let L(T) be the closed-set latice of a tree T. The lower length l, (L(T)) of L (T) is defined as Call a set S of vertices in T a sparse set if d(x, y)/> 3 for any two distinct vertices x, y in S. The sparsity y(T) of T is defined as y(T) = max {Isl: s is a sparse set of T}. We prove that, for any