Small Hop-diameter Sparse Spanners for Doubling Metrics
نویسندگان
چکیده
منابع مشابه
Greedy spanners are optimal in doubling metrics
We show that the greedy spanner algorithm constructs a (1+ )-spanner of weight −O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [11]. Our result generalizes the result by Narasimhan and Smid [15] who showed that a point set in d-dimension Euclidean space has a (1+ )-spanner of weight at most −O(d)w(MST). Our proof only uses the packing ...
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We focus on obtaining sparse representations of metrics: these are called spanners, and they have been studied extensively both for general and Euclidean metrics. Formally, a t-spanner for a metric M = (V, d) is an undirected graph G = (V,E) such that the distances according to dG (the shortest-path metric of G) are close to the distances in d: i.e., d(u, v) ≤ dG(u, v) ≤ t d(u, v). Clearly, one...
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A graph that contains a spanning tree of diameter at most t clearly admits a tree t-spanner, since a tree t-spanner of a graph G is a sub tree of G such that the distance between pairs of vertices in the tree is at most t times their distance in G. In this paper, graphs that admit a tree t-spanner of diameter at most t + 1 are studied. For t equal to 1 or 2 the problem has been solved. For t = ...
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In STOC’95 Arya et al. [2] conjectured that for any constant dimensional n-point Euclidean space, a (1+ǫ)-spanner with constant degree, diameter O(log n) and weight O(log n) ·ω(MST ) can be built in O(n · log n) time. Recently Elkin and Solomon [10] (technical report, April 2012) proved this conjecture of Arya et al. in the affirmative. In fact, the proof of [10] is more general in two ways. Fi...
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Let S be a set of n points in IR and let t > 1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and q. Such a path is called a t-spanner path. The spanner diameter of such a spanner is defined as the smallest integer D suc...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9115-5