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We show tight upper and lower bounds for time–space trade-offs for the c-Approximate Near Neighbor Search problem. For the d-dimensional Euclidean space and n-point datasets, we develop a data structure with space n 1+ρu+o(1) + O(dn) and query time n ρq+o(1) + dn o(1) for every ρ u , ρ q ≥ 0 such that: c 2 √ ρ q + (c 2 − 1) √ ρ u = 2c 2 − 1. (1) To(More)
We prove a lower bound of &#206;&#169;(<i>n</i><sup>1/3</sup>) for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function <i>f</i>:{0,1}<sup><i>n</i></sup>&#226;†’ {0,1} is monotone versus far from monotone. This improves the recent lower bound of &#206;&#169;(<i>n</i><sup>1/4</sup>) for the same problem(More)
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In particular, our lower bound matches the upper bound recently shown in [Laa15c] for the random instance on a Euclidean(More)
We prove that any non-adaptive algorithm that tests whether an unknown Boolean function f : {0, 1} n → {0, 1} is a k-junta or-far from every k-junta must make Ω(k 3/2 //) many queries for a wide range of parameters k and. Our result dramatically improves previous lower bounds from [BGSMdW13, STW15], and is essentially optimal given Blais's non-adaptive(More)
We show that every *symmetric* normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every <i>n</i>, <i>d</i> = <i>n</i><sup><i>o</i>(1)</sup>, and every <i>d</i>-dimensional symmetric norm ||Â&#183;||, there exists a data structure for (loglog<i>n</i>)-approximate nearest neighbor(More)
When analyzing the computational complexity of well-known puzzles, most papers consider the algorithmic challenge of solving a given instance of (a generalized form of) the puzzle. We take a different approach by analyzing the computational complexity of designing a " good " puzzle. We assume a puzzle maker designs part of an instance, but before publishing(More)
We give a poly(logn, 1/ε)-query adaptive algorithm for testing whether an unknown Boolean function f : {−1, 1}n → {−1, 1}, which is promised to be a halfspace, is monotone versus ε-far from monotone. Since non-adaptive algorithms are known to require almost Ω(n) queries to test whether an unknown halfspace is monotone versus far from monotone, this shows(More)
Nintendo's Mario Kart is perhaps the most popular racing video game franchise. Players race alone or against opponents to finish in the fastest time possible. Players can also use items to attack and defend from other racers. We prove two hardness results for generalized Mario Kart: deciding whether a driver can finish a course alone in some given time is(More)
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