On the Cyclic Assumption of the Cow-Path Search Algorithm

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.

Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG)

arXiv:2610.10253 [cs.DS]

(or arXiv:2610.10253v1 [cs.DS] for this version)

https://doi.org/10.48550/arXiv.2610.10253 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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