Abstract
This paper proposes strategies for maintaining a database of computational results of functions f on sequence arguments x, where x is sorted in non-decreasing order and f(x) has greatest dependence on the first few terms of x. This scenario applies also to symmetric functions f, where the partial derivatives approach zero as the corresponding component value increases. The goal is to pre-compute exact values f(u) on a tight enough net of sequence arguments, so that given any other sequence x, a neighboring sequence u in the net giving a close approximation can be efficiently found. Our scheme avoids pre-computing the more-numerous partial-derivative values. It employs a new data structure that combines ideas of a trie and an array implementation of a heap, representing grid values compactly in the array, yet still allowing access by a single index lookup rather than pointer jumping. We demonstrate good size/approximation performance in a natural application.
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References
Campbell-Kelly, M., Croarken, M., Flood, R., Robson, E.: The History of Mathematical Tables. Oxford University Press, Oxford (2003)
Muthukrishnan, S.: Data Streams: Algorithms and Applications. Now Publishers (2005)
Michie, D.: Memo functions and machine learning. Nature 218, 19–22
Liang, F.: Stochastic approximation Monte Carlo for MLP learning. In: Encyclopedia of Artificial Intelligence, pp. 1482–1489. Wiley (2009)
Regan, K., Haworth, G.McC.: Intrinsic chess ratings. In: Proceedings of AAAI 2011, San Francisco (2011)
Khoshnevisan, H., Afshar, M.: Space-efficient memo-functions. Journal of Systems and Software 35 (1996)
Khoshnevisan, H.: Efficient memo-table management strategies. Acta Informatica 28, 43–81
Alidina, M., Monteiro, J.C., Devadas, S., Ghosh, A., Papaefthymiou, M.C.: Precomputation-based sequential logic optimization for low power. IEEE Trans. VLSI Syst. 2(4), 426–436
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Biswas, T., Regan, K.W. (2014). Efficient Memoization for Approximate Function Evaluation over Sequence Arguments. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_17
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DOI: https://doi.org/10.1007/978-3-319-07956-1_17
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07955-4
Online ISBN: 978-3-319-07956-1
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