D. Aingworth, C. Chekuri, P. Indyk, R. Motwani, Fast estimation of diameter and shortest paths (without matrix mulxCwITqICJ-LT SIAM J. Comput. 28 (1999) 1167--1181.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... O(n 2 ) algorithm for finding paths with stretch at most 3, an O(n 7=3 ) algorithm for finding paths of stretch 7=3, and an O(n 3=2 m 1=2 ) algorithm for finding paths of stretch 2. The algorithms of Cohen and Zwick [6] use ideas obtained by Aingworth, Chekuri, Indyk and Motwani [2] and by Dor, Halperin and Zwick [10] that design algorithms that approximate distances in unweighted undirected graphs with a small additive error. As can be seen from their running times, these algorithms are all purely combinatorial. They do not use fast matrix multiplication algorithms. It is ....

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). To appear in SIAM Journal on Computing. A preliminary version appeared in the Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, Atlanta, Georgia, pages 547--553., 1996.

.... O(n 2 ) algorithm for nding paths with stretch at most 3, an O(n 7=3 ) algorithm for nding paths of stretch 7=3, and an O(n 3=2 m 1=2 ) algorithm for nding paths of stretch 2. The algorithms of Cohen and Zwick [CZ97] use ideas obtained by Aingworth, Chekuri, Indyk and Motwani [ACIM99] and by Dor, Halperin and Zwick [DHZ00] who designed algorithms that approximate distances in unweighted undirected graphs with a small additive error. As can be seen from their running times, these algorithms are all purely combinatorial. They do not use fast matrix multiplication algorithms. It ....

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167-1181, 1999.

....uses O(n log n) space. 1 Introduction The shortest path (SP) problem for weighted graphs with n vertices and m edges is a fundamental problem for which ecient solutions can now be found in any standard algorithms text. The approximation version of this problem has been studied extensively, see [1, 11, 14]. In numerous algorithms, query versions frequently appear as subroutines. In such a query, we are given two vertices and have to compute or approximate the shortest path between them. The latest in a series of results for undirected weighted graphs is by Thorup and Zwick [23] their algorithm ....

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167-1181, 1999.

....the maximum distance to another vertex. or (with fast matrix multiplication) complicated and impractical, and because recent applications of social network theory to the internet may involve graphs with millions of vertices, it is of interest to consider faster approximations. Aingworth et al. [1] proposed an algorithm with an additive error of 2 for the unweighted APSP problem that runs in time O(n 2.5 # log n) However this is still slow and does not provide a good approximation when the distances are small. In this paper, we consider a method for fast approximation of centrality. We ....

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication) . SIAM J. Comput. 28(4):1167--1181, 1999.

....G 0 = V; E 0 ) of G such that for every u; v 2 V we have ffi G 0 (u; v) t Deltaffi G (u; v) where ffi G (u; v) is the distance between the vertices u and v in the (possibly weighted) graph G. A different approach all together was employed recently by Aingworth, Chekuri, Indyk and Motwani [ACIM96] They describe a simple and elegant O(n 5=2 ) time algorithm for finding all distances in unweighted and undirected graphs with an additive one sided error of at most 2. They also make the very important observation that the small distances, and not the long distances, are the hardest to ....

....) time algorithm for finding all distances in unweighted and undirected graphs with an additive one sided error of at most 2. They also make the very important observation that the small distances, and not the long distances, are the hardest to approximate. Based on the ideas of Aingworth et al. ACIM96] Orlin (unpublished) obtained an O(n 7=3 ) time algorithm for finding all distances with an additive one sided error of at most 4. In this work we improve and extend the result of Aingworth et al. ACIM96] and of Orlin, and obtain an O(minfn 3=2 m 1=2 ; n 7=3 g) time algorithm, ....

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). To appear in SIAM Journal on Computing. A preliminary version appeared in the Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, Atlanta, Georgia, pages 547--553., 1996.

....used therefore for finding paths of stretch less than 3. Our approximation algorithms use a direct approach for solving the problem. They are not based on the construction of sparse spanners or sparse neighbourhood covers. Our algorithms are based on ideas used by Aingworth, Chekuri and Motwani [2] ( see also [1] for obtaining an O(n 5=2 ) time algorithm for finding allpairs surplus 2 paths in an unweighted undirected graph with n vertices. A path between two vertices u; v 2 V is said to be of surplus k if and only if its length is at most ffi(u; v) k. The O(n 5=2 ) time ....

....graphs. Algorithm APASP 4 , for example, runs in O(minfn 5=3 m 1=3 ; n 11=5 g) time and finds surplus 4 paths. As mentioned, Dor et al. 15] also obtain an O( m 2=3 n)n) time algorithm for finding all pairs stretch 3 paths in weighted graphs. The ideas used by Aingworth et al. [2] and Dor et al. 15] for obtaining additive error approximations of distances in unweighted graphs are adapted here for obtaining multiplicative error approximations of distances in weighted graphs. The algorithms presented here are simple modifications of the algorithms presented in [15] Their ....

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D. Aingworth, C. Chekuri, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, Atlanta, Georgia, pages 547--553, 1996.

....for finding paths of stretch less than 3. Our approximation algorithms use a direct approach for solving the problem. They are not based on the construction of sparse spanners or sparse neighbourhood covers. Our algorithms are based on ideas used by Aingworth, Chekuri and Motwani [2] see also [1]) for obtaining an O(n 5=2 ) time algorithm for finding allpairs surplus 2 paths in an unweighted undirected graph with n vertices. A path between two vertices u; v 2 V is said to be of surplus k if and only if its length is at most ffi(u; v) k. The O(n 5=2 ) time algorithm of ....

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). Manuscript, 1996.

...., where jd(u; v)j is the length of the shortest u Gamma v path. The approximate all pairs shortest path problem involves a tradeoff of stretch against time short paths with stretch bounded by a constant are computed in time less than it would take to compute exact all pairs shortest paths (see [1, 2, 6, 8, 9, 10]) The compact routing problem considers instead a tradeoff of stretch for space, in the setting where each node locally stores its own routing tables. The stretch of a compact routing algorithm is defined as the maximum stretch over the routes for all pairs of nodes in the network. Clearly if ....

....node i is simply a function of the routing information stored at i and the address of its final destination. The principal ingredients of our algorithm include the following: ffl The O(log n) greedy approximation to dominating set, coupled with truncated and full Dijkstra s algorithms as used in [1, 2, 9, 10] and in the same fashion as to how it is used in [4] ffl A new density dependent algorithm for landmark selection. It is possible to give a careful distributed implementation of our algorithms, along the same lines as in [5] The improvements we present are at the algorithmic, not at the protocol ....

D. Aingworth, C. Chekuri, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). In Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pages 547--553, Atlanta, Georgia, 28--30 Jan. 1996. 6

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D. Aingworth, C. Chekuri, P. Indyk, R. Motwani, Fast estimation of diameter and shortest paths (without matrix mulxCwITqICJ-LT SIAM J. Comput. 28 (1999) 1167--1181.

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D. Aingworth,C. Chekuri,P. Indyk, and R. Motwani, Fast estimation of diameter and shortest paths(withou matrix mu();)#P(+=+6#u SIAM J. onCom puting, 28 (1999), 1167--1181.

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Aingworth, D., Chekuri, C., Indyk, P., and Motwani, R. Fast estimation of diameter and shortest paths (without matrix multiplication) . SIAM Journal on Computing 28, 4 (1999), 1167--1181.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani, Fast estimation of diameter and shortest paths (without matrix multiplication), SIAM J Comput 28 (1999), 1167--1181.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167--1181, 1999. 11

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167--1181, 1999.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J. Computing, 28:1167--1181, 1999.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167--1181, 1999.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167-1181, 1999.

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Aingworth, D., Chekuri, C., Indyk, P., and Motwani, R. Fast estimation of diameter and shortest paths (without matrix multiplication) . SIAM Journal on Computing 28, 4 (1999), 1167--1181.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167--1181, 1999.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani, Fast estimation of diameter and shortest paths(without matrix multiplication), SIAM Journal on Computing 28 (1999), no. 4, 1167--1181.

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D. Aingworth, C. Chekuri, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication) . In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, Atlanta, Georgia, pages 547-- 553, 1996.

No context found.

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). Manuscript, 1996.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167-1181, 1999.

No context found.

D. Aingworth, C. Chekuri, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 547--553, 1996.

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D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani, Fast estimation of diameter and shortest paths (without matrix multiplication), SIAM J. Comput. 28 (1999), pp. 1167--1181

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