P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. ACM Symposium on Discrete Algorithms, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....dense point sets in IR d , which have spread O(n 1=d ) Valtr and others [33, 59, 60, 61, 62] have established several combinatorial results for dense point sets that improve corresponding bounds for arbitrary point sets. For other combinatorial and algorithmic results related to spread, see [15, 23, 37, 41, 42, 47]. In Section 2, we prove that the Delaunay triangulation of any set of n points in IR 3 with spread has complexity O( 3 ) In particular, the Delaunay triangulation of any dense point set in IR 3 has only linear complexity. This bound is tight in the worst case for all = O( p n) and ....

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. Proc. 8th Annu. ACM-SIAM Sympos. Discrete Algorithms, 457-465, 1999.

....abstract version of the problem is that of finding the LCP of two 3 D point sets with exact congruence replaced by ffl congruence. Closely related problems, involving both exact and also ffl congruence have been extensively studied in computational geometry, references to which can be found in [6, 13]. There is also a large body of literature on computational chemistry which address the substructure identification problem, an overview of which can be obtained from [9] and the references therein. However, none of them are systematic, but are based on some heuristic. Moreover, they do not ....

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. In Proc. 10th. Annual ACM-SIAM Symp. on Discrete Algorithms, 1999.

.... and d dimensional point sets, and the underlying metrics being L1 , L 1 and L 2 [11, 12, 18] In an e ort to improve the running time, various approximation algorithms for either the Hausdor or the bottleneck metric for point sets in two, three, and in general d dimensions have been presented in [9, 10, 15 17, 19, 20, 22]. Pattern matching using bottleneck metric It should be noted that most of the known exact algorithms, especially those involving three and higher dimensional point sets, are restricted to either the exact or the Hausdor metric. While the exact metric is ill posed for many practical ....

....metric can be adapted for computing the bottleneck matching. Neither do the algorithms of [5] extend from the planar case to work in three or higher dimensions in any simple way. Very recently, a new paradigm for point set pattern matching based on algebraic convolutions was proposed in [9] and [19]. This reduced the complexity of the problem under Hausdor metric to nearly quadratic time. However, as noted in [20] the one to one restriction imposed by bottleneck matching distance seems not to t well within the rigid framework of algebraic convolutions . Our results In this paper we ....

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. In Proc. 10th. Annual ACM-SIAM Symp. on Discrete Algorithms, pages 457-465, 1999.

....in the plane in time O(N 2 k log N ) and approximation factor 8 (for any fixed 0) in R 3 in time O(N 3 k logN ) De Rezende and Lee described an O(N d k) time solution to the Exact Rigid Motion problem. Recently and independently of our work, Indyk, Motwani and Venkatasubramanian [19] studied the rigid motions problem in its Threshold (hence also Nearly Exact or Approximate Best Match) formulation in two and three dimensions, with and without point failures. Their runtimes (omitting log terms as well as the dependence on a precision parameter and on the value of the threshold) ....

P. Indyk, R. Motwani and S. Venkatasubramanian, Geometric Matching Under Noise: Combinatorial Bounds and Algorithms. To appear in Proc. 10'th SIAM-ACM Symp. Discr. Alg., 1999.

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Piotr Indyk, Rajeev Motwani, and Suresh Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. Proc. of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, 1999.

.... Total Square Di erence, de ned as is readily computed in O(n log m) time for all alignments of a length m pattern with a length n text (simply note that = i=1 u(i) i=1 v(i) i=1 u(i)v(i) 18] Subsequently, Indyk and others discovered additional applications for Subset Matching [14]. Our Result. Our main result in this paper is an O(s log s) time deterministic algorithm, an O(s ) time randomized Las Vegas algorithm, and an O(s log s) time randomized Monte Carlo algorithm, for the Subset Matching problem. In conjunction with the above mentioned linear time reduction ....

P. Indyk, R. Motwani, S. Venkatasubramanian, Geometric matching under noise: combinatorial bounds and algorithms. Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, 1999, pp. 457-465.

.... a linear reduction from Tree Pattern Matching to Subset Matching and provided O(n log 3 n) time randomized algorithm for the latter problem [CH97] n denotes the size of the input) Subsequently, Indyk and others discoved several other applications for Subset Matching and its special cases [Ind97, IMV98]. See Section 1.1 for more description of previous and related work. In this paper we give an O(n log 3 n) time deterministic algorithm for the the Subset Matching problem. This improves an earlier bound of O(n 1 o(1) by Indyk [Ind97] and immediately yields an algorithm of the same e#ciency ....

P. Indyk, R. Motwani, S. Venkatasubramanian, "Geometric Matching Under Noise: Combinatorial Bounds and Algorithms", these proceedings.

.... the (generalized) Hausdorff distance between two point sets in 2 and 3 dimensions (usually under translations and rigid motions) has been studied extensively [7, 13, 24] see also the survey by Alt and Guibas [3] The approximate versions of the above problems have also been investigated [1, 16, 5]. In particular, the combination of the results of [1] and [5] results in an O(s log s) time algorithm for estimating (up to any constant factor) the Hausdorff distance of sets from H s T (l 2 2 ) where T is the set of all rigid motions. Finally, we consider another derived metric similar to ....

Piotr Indyk, Rajeev Motwani, and Suresh Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. Proc. of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, 1999.

.... a linear reduction from Tree Pattern Matching to Subset Matching and provided O(n log 3 n) time randomized algorithm for the latter problem [CH97] n denotes the size of the input) Subsequently, Indyk and others discoved several other applications for Subset Matching and its special cases [Ind97, IMV98]. See Section 1.1 for more description of previous and related work. In this paper we give an O(n log 3 n) time deterministic algorithm for the the Subset Matching problem. This improves an earlier bound of O(n 1 o(1) by Indyk [Ind97] and immediately yields an algorithm of the same ....

P. Indyk, R. Motwani, S. Venkatasubramanian, "Geometric Matching Under Noise: Combinatorial Bounds and Algorithms", these proceedings.

....of points p; q 2 H d , consider the similarity measure D(p; q) defined as the dot product p Delta q. The dot product is a common measure used in information retrieval applications [32] it is also of use in molecular clustering [14] By using techniques by Indyk, Motwani, and Venkatasubramanian [41] it can also be used for solving the approximate largest common point set problem, which has many applications in image retrieval and pattern recognition. By a simple substitution of parameters, we can prove that for a set of binary vectors of approximately the same weight, PLEB under dot product ....

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric Matching Under Noise - Combinatorial Bounds and Algorithms. Manuscript, 1997.

.... shown that it is possible to approximate the Hausdorff distance in two dimensions to within small constant factors using a natural heuristic which aligns a fixed pair of points from the pattern to all point pairs from the image; the running time of the algorithm is O(kn 2 ) In our recent paper [IMV99] we give a more detailed analysis of the alignment scheme, presenting an algorithm that approximates the Hausdorff distance under the model defined by Heffernan and Schirra [HS94] where the goal is to obtain a solution close to a predefined threshold ffl. In addition, our work [IMV99] also ....

....paper [IMV99] we give a more detailed analysis of the alignment scheme, presenting an algorithm that approximates the Hausdorff distance under the model defined by Heffernan and Schirra [HS94] where the goal is to obtain a solution close to a predefined threshold ffl. In addition, our work [IMV99] also presented a new paradigm which obtains the best known algorithms for the approximate version of the problem by transforming it to combinatorial pattern matching; independently, a similar paradigm was presented by Cardoze and Schulman [CS98] For a point set P , let the diameter of P , ....

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P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. In 10th Annual SIAM-ACM Symposium on Discrete Algorithms, 1999.

....2 ) randomized) when ff is known for 3D. In 2D, the corresponding bounds obtained are O(n 3:2 ) and O(n 2:2 =ff) However, these bounds apply only to the noise free model of point sets. The noisy version of the problem was considered in [2] yielding an O(n 8 ) algorithm in 2D. Refer to [14] for recent results in the noisy model. We now describe two random sampling schemes for solving LCP ff on noisy data. Our analysis (presented in [10] assumes that the data is exact. We use the notation g(n) O(f(n) where f and g are functions, to indicate that g(n) O(f(n) log n) Also ....

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. Manuscript.

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P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. ACM Symposium on Discrete Algorithms, 1999.

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P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. In ##### #### ###### ##### ### ######### ## ######## ##########, 1999.

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P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. ACM Symposium on Discrete Algorithms, 1999.

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P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: combinatorial bounds and algorithms. In Symposium on Discrete Algorithms (SODA), pages 457--465, 1999.

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P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: combinatorial bounds and algorithms. In Symposium on Discrete Algorithms (SODA), pages 457--465, 1999.

No context found.

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: combinatorial bounds and algorithms. In Symposium on Discrete Algorithms (SODA), pages 457--465, 1999.

No context found.

P. Indyk, R. Motwani, and S. Venkatasubramanian. Geometric matching under noise: Combinatorial bounds and algorithms. In Proc. 10th ACM-SIAM Symposium on Discrete Algorithms, pages 457-465, 1999.

No context found.

P. Indyk, R. Motwani and S. Venkatasubramanian, Geometric Matching Under Noise: Combinatorial Bounds and Algorithms. To appear in Proc. 10'th SIAM-ACM Symp. Discr. Alg., 1999.

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