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Computing All Best Swaps for . . .
, 2010
"... In a densely connected communication network, represented by a graph G with nonnegative edge weights, it is often advantageous to route all communication on a sparse spanning subnetwork, typically a spanning tree of G. We consider a tree spanner T of G which guarantees that for any two nodes, their ..."
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edge in the spanner T, a best swap edge that minimizes the stretch of the new tree. We show how all these best swap edges
Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
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Cited by 350 (32 self)
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The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized
Collective tree spanners of graphs
 SWAT 2004
, 2004
"... In this paper we introduce a new notion of collective tree spanners. We say that a graph G =(V,E) admits a system of µ collective additive tree rspanners if there is a system T (G) of at most µ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈T(G) exists such that d ..."
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Cited by 14 (10 self)
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In this paper we introduce a new notion of collective tree spanners. We say that a graph G =(V,E) admits a system of µ collective additive tree rspanners if there is a system T (G) of at most µ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈T(G) exists
AN OPTIMAL ALGORITHM FOR COMPUTING ANGLECONSTRAINED SPANNERS
 JOURNAL OF COMPUTATIONAL GEOMETRY
"... Let S be a set of n points in R d and let t> 1 be a real number. A graph G = (S, E) is called a tspanner for S, if for any two points p and q in S, the shortestpath distance in G between p and q is at most tpq, where pq  denotes the Euclidean distance between p and q. The graph G is called ..."
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Cited by 3 (3 self)
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θangleconstrained, if any two distinct edges sharing an endpoint make an angle of at least θ. It is shown that, for any θ with 0 < θ < π/3, a θangleconstrained tspanner can be computed in O(n log n) time, where t depends only on θ. For values of θ approaching 0, we have t = 1 + O(θ).
Local Computation of Nearly Additive Spanners
"... An (α, β)spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u, v, dH(u, v) ≤ α ·dG(u, v)+β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α, β) ..."
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Cited by 6 (3 self)
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parameters, this algorithm provides a (2k − 1, 0)spanner of at most kn 1+1/k edges in k rounds, matching the performances of the best known distributed algorithm by Derbel et al. (PODC ’08). For k = 2 and constant ε> 0, it can also produce a (1+ε,2−ε)spanner of O(n 3/2) edges in constant time. More
Optimal Spanners in Partial kTrees
, 1993
"... Assume you have a problem K which is NPhard in general, but in P for a certain class of graphs G. Let PatchG be a class of graphs which are `patched' together from graphs from G. Is membership in K "PatchG now in P ? We show that for K t , the problem of finding optimal tspanners, G ce ..."
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Assume you have a problem K which is NPhard in general, but in P for a certain class of graphs G. Let PatchG be a class of graphs which are `patched' together from graphs from G. Is membership in K "PatchG now in P ? We show that for K t , the problem of finding optimal tspanners, G
tSpanners for Metric Space Searching ⋆
"... The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a tspanner G ′ (V,E) as the representation of the metric datab ..."
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The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a tspanner G ′ (V,E) as the representation of the metric
Construction of minimumweight spanners
 In Proc. of the 12th European Symposium on Algorithms
, 2004
"... Abstract. Spanners are sparse subgraphs that preserve distances up to a given factor in the underlying graph. Recently spanners have found important practical applications in metric space searching andmessage distribution in networks. These applications use some variant of the socalled greedy algori ..."
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Cited by 2 (0 self)
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algorithm for constructing the spanner — an algorithm that mimics Kruskal’s minimum spanning tree algorithm. Greedy spanners have nice theoretical properties, but their practical performance with respect to total weight is unknown. In this paper we give an exact algorithm for constructing minimum
Tree Spanners in Planar Graphs
 DISCRETE APPLIED MATHEMATICS
, 1998
"... A tree tspanner of a graph G is a spanning subtree T of G in which the distance between every pair of vertices is at most t times their distance in G. Spanner problems have received some attention, mostly in the context of communication networks. It is known that for general unweighted graphs, ..."
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A tree tspanner of a graph G is a spanning subtree T of G in which the distance between every pair of vertices is at most t times their distance in G. Spanner problems have received some attention, mostly in the context of communication networks. It is known that for general unweighted graphs
Results 1  10
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