D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167--176, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....algorithm is distributed. We assign to each vertex of the network a distance or reachability label such that we can later calculate the distance (or reachability relation) between two vertices using only the labels of these two vertices. Distance labels were considered, among others, by Peleg [10], Gavoille et al. 4] and Thorup and Zwick [12] All these papers, however, consider only undirected graphs, and only worst case results. We are interested mainly in directed graphs, and in the performance of the proposed labeling scheme on networks that occur in practice. Our labels are based on ....

D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167--176, 2000.

....algorithm is distributed. We assign to each vertex of the network a distance or reachability label such that we can later calculate the distance (or reachability relation) between two vertices using only the labels of these two vertices. Distance labels were considered, among others, by Peleg [10], Gavoille et al. 4] and Thorup and Zwick [12] All these papers, however, consider only undirected graphs , and only worst case results. We are interested mainly in directed graphs, and in the performance of the proposed labeling scheme on networks that occur in practice. Our labels are based ....

D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167--176, 2000.

....to the row of the distance matrix of G. So the dimension of U n gives an upper bound on the number of di erent labels needed to label every vertex of every n vertex graph of F . Labeling of a graph with such implicit distance computation capabilities is called distance labeling scheme. Formally [Pel00b] a distance labeling scheme for a graph family F is a pair hL; fi of functions such that L(v; G) is a binary label associated to the vertex v in the graph G, and such that f(L(x; G) L(y; G) returns the distance between the vertices x and y in the graph G, for all x; y of G and every G 2 F . ....

D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167-176, 2000.

....satis es that there is a tree, and a node x of that tree, for which length(address(x) length(data(x) 350 n= log log n) The remaining of the paper is dedicated to proving Theorem 1. The proof is based on the following de nition which belongs to the informative labeling theory (cf. [10, 11, 12] and [9] for an overview) De nition 1 Given a family F of graphs, a forwarding labeling on F is a pair (L; R) where R is called the routing function, and L is called the labeling function. For every G 2 F and every node x of G, L assigns a non empty binary string L(x) to x, and, for any two ....

....cance of the result in regard with previous upper bounds for routing in trees and in arbitrary networks, this result must also be compared to the best upper bound on the memory requirement for shortest path routing in graphs of bounded treewidth. Up to our knowledge, the best result is due to [12] where it is shown that there exists a shortest path routing scheme for graphs on treewidth k using addresses and local data structures of size n) For tree (treewidth 1) this bound is not tight, by a factor log log. We hence let as an open problem the question of whether one can design (under ....

David Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167{ 176, 2000.

....path routing in trees because it is possible to de ne compact routing scheme on trees that are not along the shortest route, e.g. see [2] The remaining of the paper is dedicated to proving Theorem 1. The proof is based on the following de nition from the informative labeling theory (cf. [10 12] and [9] for an overview) De nition 1. Given a family F of graphs, a forward labeling on F is a pair (L; R) where R is called the routing function, and L is called the labeling function. For every G 2 F and every node x of G, L assigns a non empty binary string L(x) to x, and, for any two ....

....cance of the result in regard with previous upper bounds for routing in trees and in arbitrary networks, this result must also be compared to the best upper bound on the memory requirement for shortest path routing in graphs of bounded treewidth. Up to our knowledge, the best result is due to [12] where it is shown that there exists a shortest path routing scheme for graphs on treewidth k using addresses and local data structures of size O(k log 2 n) For tree (treewidth 1) this bound is not tight, by a factor log log. We hence leave as an open problem the question of whether one can ....

David Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167-176, 2000.

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D. Peleg, Proximity-preserving labeling schemes, J. Graph Theory 33 (2000) 167--176.

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D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167--176, 2000.

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D. Peleg. Proximity-preserving labeling schemes. J. Graph Theory, 33:167--176, 2000.

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David Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167-176, 2000.

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D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, (33):167--176.

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David Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167-176, 2000.

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David Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167-176, 2000.

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D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167--176, 2000.

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D. Peleg. Proximity-preserving labeling schemes. Journal of Graph Theory, 33:167-176, 2000.

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