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- research-articleJanuary 2020
Algorithmic Polynomials
SIAM Journal on Computing (SICOMP), Volume 49, Issue 62020, Pages 1173–1231https://doi.org/10.1137/19M1278831The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, ...
- research-articleJanuary 2020
Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds
SIAM Journal on Computing (SICOMP), Volume 49, Issue 62020, Pages 1128–1172https://doi.org/10.1137/17M1118014Local search proved to be an extremely useful tool when facing hard optimization problems (e.g., via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially ...