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arXiv · 2610.10253

On the Cyclic Assumption of the Cow-Path Search Algorithm

Yuan Ma·Yiqun Lisa Yin
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Abstract

In the cow-path problem, a cow must find a goal lying at an unknown distance on one of $w$ paths connected only at the origin, and performance is measured by competitive ratio. Kao, Reif and Tate designed an efficient randomized algorithm in which the cow visits the paths in a fixed cyclic order. They proved the algorithm is optimal for $w=2$, and subsequently Kao, Ma, Sipser and Yin proved its optimality for all $w$, with a claim that no algorithm does better than the best cyclic one. This note provides a detailed proof of that claim.

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Yuan Ma, Yiqun Lisa Yin. 2026-10-07. On the Cyclic Assumption of the Cow-Path Search Algorithm. https://arxiv.org/abs/2610.10253

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