A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Journal of Symbolic Computation - Special issue on computational algebraic complexity
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SIAM Journal on Computing
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SIAM Journal on Computing
Algorithms for computing sparse shifts for multivariate polynomials
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
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Journal of the ACM (JACM)
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AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
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Proceedings of the 2002 international symposium on Symbolic and algebraic computation
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Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
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Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
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Theoretical Computer Science
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Proceedings of the 36th international symposium on Symbolic and algebraic computation
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Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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ACM Transactions on Algorithms (TALG)
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We give a new class of algorithms for computing sparsest shifts of a given polynomial. Our algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the early termination test. Through reformulating as multivariate shifts in a designated set, our algorithms can compute the sparsest shifts that simultaneously minimize the terms of a given set of polynomials. Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and potentially to other bases as well. For a given univariate polynomial, we give a lower bound for the optimal sparsity. The efficiency of our algorithms can be further improved by imposing such a bound and pruning the highest degree terms.