منابع مشابه
New Results on Fault Tolerant Geometric Spanners
We investigate the problem of constructing spanners for a given set of points that are tolerant for edge/vertex faults. Let S IRd be a set of n points and let k be an integer number. A k-edge/vertex fault tolerant spanner for S has the property that after the deletion of k arbitrary edges/vertices each pair of points in the remaining graph is still connected by a short path. Recently it was sho...
متن کاملFault-Tolerant Additive Weighted Geometric Spanners
Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance dw(p, q) between two points p, q ∈ S is defined as w(p) + d(p, q) + w(q) if p 6= q and it is zero if p = q. Here, d(p, q) denotes the (geodesic) Euclidean distance between p and q. A graph G(S,E) is called a t-spanner for the additive weighted set S of points if fo...
متن کاملImproved Purely Additive Fault-Tolerant Spanners
Let G be an unweighted n-node undirected graph. A βadditive spanner of G is a spanning subgraph H of G such that distances in H are stretched at most by an additive term β w.r.t. the corresponding distances in G. A natural research goal related with spanners is that of designing sparse spanners with low stretch. In this paper, we focus on fault-tolerant additive spanners, namely additive spanne...
متن کاملFault-Tolerant Spanners in Networks with Symmetric Directional Antennas
Let P be a set of points in the plane, each equipped with a directional antenna that covers a sector of angle α and range r. In the symmetric model of communication, two antennas u and v can communicate to each other, if and only if v lies in u’s coverage area and vice versa. In this paper, we introduce the concept of fault-tolerant spanners for directional antennas, which enables us to constru...
متن کاملFault-Tolerant Spanners for Doubling Metrics: Better and Simpler
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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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1121-7