منابع مشابه
Transforming spanning trees: A lower bound
For a planar point set we consider the graph of crossing-free straight-line spanning trees where two spanning trees are adjacent in the graph if their union is crossing-free. An upper bound on the diameter of this graph implies an upper bound on the diameter of the flip graph of pseudo-triangulations of the underlying point set. We prove a lower bound of Ω ( log(n)/ log(log(n)) ) for the diamet...
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Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T ′ of TS are adjacent if T intersects T ′ only in points of S or in common edges. We prove that the diameter of TS is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the flip graph PS of pseudo-triangulations...
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This paper presents a new method for computing the lower bounds for multihop network design problems which is particularly well suited to optical networks. More speciically, given N stations each with d transceivers and pairwise average traac values of the stations, the method provides a lower bound for the combined problem of nding optimum (i) allocation of wavelengths to the stations to deter...
متن کامل1 Lower Bound on Coloring Rooted Trees
Definition 1. (The LOCAL model) We consider an arbitrary n-node graph G = (V,E) where V = {1, 2, . . . , n}, which abstracts the communication network. Unless noted otherwise, G is a simple, undirected, and unweighted graph. There is one process on each node v ∈ V of the network. At the beginning, the processes do not know the graph G, except for knowing n, and their own unique identifier in {1...
متن کاملLower Bound on Coloring Rooted Trees
Definition 1. (The LOCAL model) We consider an arbitrary n-node graph G = (V,E) where V = {1, 2, . . . , n}, which abstracts the communication network. Unless noted otherwise, G is a simple, undirected, and unweighted graph. There is one process on each node v ∈ V of the network. At the beginning, the processes do not know the graph G, except for knowing n, and their own unique identifier in {1...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2009
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2008.03.005