منابع مشابه
Leafy spanning trees in hypercubes
Given an undirected graph G V E the problem of nding a spanning tree T of G with the maximum number of leaves is NP Complete Constant factor approximation algorithms are known for this problem but the problem does not admit a polynomial time approximation scheme unless P NP Kleitman and West gave a lower bound of ln n on the function l n which is de ned as the minimum of the maximum number of l...
متن کاملOptimal Independent Spanning Trees on Hypercubes
Two spanning trees rooted at some vertex r in a graph G are said to be independent if for each vertex v of G, v ≠ r, the paths from r to v in two trees are vertex-disjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. A set of independent spanning trees is optimal if the average path length of the trees is the minimum. Any k-dimensional hypercube has ...
متن کاملThe Transformation of Optimal Independent Spanning Trees in Hypercubes∗
Multiple spanning trees rooted at the same vertex, say r, of a given graph are said to be independent if for each non-root vertex, say v, paths from r to v, one path in each spanning trees, are internally disjoint. It has been proved that there exist k optimal independent spanning trees (OIST for short) rooted at any vertex in the k-dimensional hypercube. The word optimal is defined by an addit...
متن کاملLeafy Spanning
We prove that the d-dimensional hypercube, Hd, with n = 2 d vertices, contains a spanning tree with at least 1 ? 2 log 2 n ? o 1 log n n + 2 leaves. This improves upon the bound implied by a more general result on spanning trees in graphs with minimum degree , which gives 1 ? O(log log n) log 2 n n as a lower bound on the maximum number of leaves in spanning trees of n-vertex hypercubes.
متن کاملIndependent Spanning Trees on Systems-on-chip Hypercubes Routing
Independent spanning trees (ISTs) provide a number of advantages in data broadcasting. One can cite the use in fault tolerance network protocols for distributed computing and bandwidth. However, the problem of constructing multiple ISTs is considered hard for arbitrary graphs. In this paper we present an efficient algorithm to construct ISTs on hypercubes that requires minimum resources to be p...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2001
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(01)00047-7