Pointer chasing via triangular discrimination

Abstract

Abstract We prove an essentially sharp $\tilde \Omega (n/k)$ lower bound on the k -round distributional complexity of the k -step pointer chasing problem under the uniform distribution, when Bob speaks first. This is an improvement over Nisan and Wigderson’s $\tilde \Omega (n/{k^2})$ lower bound, and essentially matches the randomized lower bound proved by Klauck. The proof is information-theoretic, and a key part of it is using asymmetric triangular discrimination instead of total variation distance; this idea may be useful elsewhere.

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