Abstract
In this paper a deterministic algorithm for the length reduction problem is presented. This algorithm enables a new tool for performing fast convolution in sparse data. The proposed algorithm performs the convolution in \(O(n_1 \log^3 n_1)\), where n 1 is the number of non-zero values in V 1. This algorithm assumes that V 1 is given in advance, and the V 2 is given in running time.
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References
Berrizbeitia, P.: Sharpening primes is in p for a large family of numbers (November 2002), http://arxiv.org/abs/math.NT/0211334
Gottesfeld Brown, L.: A survey of image registration techniques. ACM Computing Surveys 24(4), 325–376 (1992)
Cheung, K.-W., Yeung, D.-Y., Chin, R.T.: Bidirectional deformable matching with application to handwritten character extraction. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(8), 1133–1139 (2002)
Cole, R., Hariharan, R.: Verifying candidate matches in sparse and wildcard matching. In: Proc. 34st Annual Symposium on the Theory of Computing (STOC), pp. 592–601 (2002)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, McGraw-Hill, Cambridge (1992)
Kavraki, L.: Pharmacophore identification and the unknown receptor problem. J Comput Aided Mol Des. 16(8-9), 653–681 (2002)
Muthukrishnan, S.: New results and open problems related to non-standard stringology. In: Galil, Z., Ukkonen, E. (eds.) Combinatorial Pattern Matching. LNCS, vol. 937, pp. 298–317. Springer, Heidelberg (1995)
Rucklidge, W.J.: Efficient visual recognition using the hausdorff distance. Springer, Heidelberg (1996)
Schulman, L., Cardoze, D.: Pattern matching for spatial point sets. In: Proc. 39th IEEE FOCS, pp. 156–165 (1998)
Ukkonen, E., Lemström, K., Mäkinen, V.: Sweepline the music! In: Klein, R., Six, H.-W., Wegner, L. (eds.) Computer Science in Perspective. LNCS, vol. 2598, pp. 330–342. Springer, Heidelberg (2003)
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Amir, A., Kapah, O., Porat, E. (2007). Deterministic Length Reduction: Fast Convolution in Sparse Data and Applications. In: Ma, B., Zhang, K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73437-6_20
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DOI: https://doi.org/10.1007/978-3-540-73437-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73436-9
Online ISBN: 978-3-540-73437-6
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