WebWe then provide a new analysis showing that the original Morris Counter itself, after a minor but necessary tweak, actually also enjoys this same improved upper bound. Lastly, we prove a new lower bound for this task showing optimality of our upper bound. We thus completely resolve the asymptotic space complexity of approximate counting. WebOptimal Bounds for Approximate Counting. Jelani Nelson, Huacheng Yu. Computer Science; ... We thus completely resolve the asymptotic space complexity of approximate counting. Furthermore all our constants are explicit, and our lower bound and tightest upper bound differ by a multiplicative factor of at most 3+o(1). ... approximate counting ...
Quantum Approximate Counting, Simplified - The Society for …
WebWe then provide a new analysis showing that the original Morris Counter itself, after a minor but necessary tweak, actually also enjoys this same improved upper bound. Lastly, we … WebOptimal Bounds for Approximate Counting ... asymptotic space complexity of approximate counting. Furthermore all our constants are explicit, and our lower bound and tightest … rism directory
Applying Approximate Counting for Computing the Frequency
WebThis is optimal, matching the straightforward protocols where the witness is either empty, or speci es all the elements of S. ... We demonstrate the power of these lower bound techniques by proving optimal lower bounds for the approximate counting problem, which captures the following task. Given a nonempty nite set S [N] := f1;:::;Ng, estimate ... WebQuantum Lower Bounds for Approximate Counting via Laurent Polynomials Scott Aaronsony Robin Kothariz William Kretschmerx Justin Thaler{Abstract We study quantum algorithms that ar Webof deterministic approximate counting algorithms in Weitz’s work [31], strong spatial mixing was already a widely studied notion in computer science and mathematical physics for its utility in analyzing the mixing time of Markov chains [10,18,19], and hence an improved understanding of conditions under which it holds is of interest in its own ... rism cwu