D. Cardoze and L. Schulman. Pattern matching for spatial point sets. In ##### #### ###### ######### ## ### ########### ## ######## #######, pages 156{ 165. IEEE, November 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....number of non wildcards in p must be at most k for it to occur anywhere in the text. We assume that both the text and the pattern are given by the implicit O(kd) size description which speci es the list of non zero entries in each. This problem was de ned (implicitly) by Cardoze and Schulman [2] with the aim of solving the Geometric Pattern Matching problem (which will be de ned shortly) They gave a Monte Carlo randomized algorithm with running time O(k log k kd) and failure probability inverse polynomial in k. The key idea in this algorithm was to hash the text and pattern down to ....

....md n, a variant of the standard trick of breaking the text into smaller pieces decreases this running time to The failure probability is inverse polynomial in minfk; dm) g. Our Las Vegas algorithm essentially adds a veri cation step to the Monte Carlo algorithm of Cardoze and Schulman [2]. Veri cation requires the detection of spurious matches introduced by the hashing mentioned above. To detect such matches, one needs to check whether each pair of aligned characters (in the text and pattern obtained after hashing) in a claimed match actually corresponds to a pair of aligned ....

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D. Cardoze, L. Schulman. Pattern Matching for Spatial Point Sets. Proceedings of the 39th IEEE Symposium on Foundations of Computer Science, 1998, pp. 156-165.

....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 ....

D. E. Cardoze and L. Schulman. Pattern matching for spatial point sets. Proc. 39th Annu. IEEE Sympos. Found. Comput. Sci., 156-165, 1998.

....of S; a translation of P ; a rotation of P ; congruent, or similar, to P ; approximately congruent to P ; a maximal cardinality subset of P that is congruent or similar to a subset of S; etc. Among the papers in which such variants of the Point Set Pattern Matching problem have been studied are [2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 16, 17, 19, 20]. For the exact matching (i.e. nding all congruent copies of) version of the PSPM Problem, the fastest sequential algorithms in the literature are the following. Department of Computer and Information Sciences, Niagara University, Niagara University, NY 14109, USA. e mail: boxer niagara.edu. ....

D.E. Cardoze and L.J. Schulman, \Pattern matching for spatial point sets," Proceedings Symposium on Foundations of Computer Science, 1998, 156-165. 19

....measure in the plane under translations. Goodrich et al. ( GMO94] obtain simple algorithms that yield constant factor approximations for PM under the Hausdorff measure in two and three dimensions under different transformation groups. Recently and independently of our work, Cardoze and Schulman [SC98] presented a set of randomized algorithms for approximate PM and LCP under the Hausdorff measure in d dimensions 1 Technically, none of these three measures satisfy the property of being a metric. 2 We use O(f(n) to denote O(f(n) log O(1) n) and o(f(n) to denote O(f(n) log (1) ....

L. Schulman and D. Cardoze. Pattern matching for spatial point sets. In Thirty-ninth Annual Symposium on the Foundations of Computer Science. IEEE, November 1998.

.... 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 ....

....Hausdor 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 ....

D.E. Cardoze and L.J. Schulman. Pattern matching for spatial point sets. In Proc. 39th Annual Symposium on Foundations of Computer Science, pages 156{ 165, 1998.

.... with application to areas such as computer vision [22] pattern recognition [6, 13] and computational chemistry [11, 12, 23] Thus the problem of computing (exactly or approximately) the Hausdorff distance between two point sets P and Q in two and three dimensions has been studied extensively [1, 5, 6, 13, 24] with the interesting problems being those where one set can be rotated or translated and one seeks the transform which minimizes the Hausdorff distance. Unfortunately, no efficient algorithms have been designed for the case when we want to match P with many Q s and find the closest one. This ....

.... 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 ....

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David Cardoze and Leonard Schulman. Pattern matching for spatial point sets. Proc. of the 39th IEEE Annual Symp. on Foundation of Computer Science, 1998.

....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 , diam(P) maxp 1 ;p 2 2P kp1 Gamma p2k. If the diameters of both P and Q are bounded (say by Delta) then the running times of these algorithms are respectively O(n(n Delta)polylog n) IMV99] or even O(n 2 log n log O(1) Delta) CS98] ....

....[CS98] For a point set P , let the diameter of P , diam(P) maxp 1 ;p 2 2P kp1 Gamma p2k. If the diameters of both P and Q are bounded (say by Delta) then the running times of these algorithms are respectively O(n(n Delta)polylog n) IMV99] or even O(n 2 log n log O(1) Delta) CS98] 1 . In this paper, we undertake a detailed performance comparison of these recent schemes. In particular we investigate the performance of the following algorithms: BA: An alignment scheme based on the work of Goodrich et al. [GMO94] MGRID: The alignment based scheme from [IMV99] GRID: A ....

D. Cardoze and L. Schulman. Pattern matching for spatial point sets. In Thirty-ninth Annual Symposium on the Foundations of Computer Science. IEEE, November 1998.

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D. Cardoze and L. Schulman. Pattern matching for spatial point sets. In ##### #### ###### ######### ## ### ########### ## ######## #######, pages 156{ 165. IEEE, November 1998.

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David Cardoze and Leonard Schulman. Pattern matching for spatial point sets. Proc. of the 39th IEEE Annual Symp. on Foundation of Computer Science, 1998.

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D. Cardoze and L. Schulman. Pattern matching for spatial point sets. In Proc. 39th Annu. IEEE Sympos. Found. Comput. Sci., pages 156-165, 1998.

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