On generating all maximal independent sets
Information Processing Letters
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Generating all maximal models of a Boolean expression
Information Processing Letters
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
The np-completeness of the hamiltonian cycle problem in planar diagraphs with degree bound two
Information Processing Letters
Approximate verification and enumeration problems
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
Enumerating with constant delay the answers to a query
Proceedings of the 16th International Conference on Database Theory
On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
Theory of Computing Systems
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We study the problem of generating monomials of a polynomial in the context of enumeration complexity. We present two new algorithms for restricted classes of polynomials, which have a good delay between two generated monomials and the same global running time as the classical ones. Moreover they are simple to describe, use small evaluation points and one of them is parallelizable. We introduce TotalPP, IncPP and DelayPP, which are probabilistic counterparts of the most common classes for enumeration problems, hoping that randomization will be a tool as strong for enumeration as it is for decision. Our interpolation algorithms prove that a few interesting problems are in these classes like the enumeration of the spanning hypertrees of a 3-uniform hypergraph. Finally we give a method to interpolate degree 2 polynomials with an acceptable (incremental) delay. We also prove that finding a specified monomial in a degree 2 polynomial is hard unless RP = NP. It suggests that there is no algorithm with a delay as good (polynomial) as the one we achieve for multilinear polynomials.