A proof of Ross's conjecture for two-site moving-target search

Yunpeng Li

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arXiv · 2608.09368

A proof of Ross's conjecture for two-site moving-target search

Yunpeng Li

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Abstract

A target moves between two sites according to a discrete-time Markov chain with a $2\times2$ transition matrix $M$. At each epoch one site is searched at positive cost, and a search may overlook a target that is present. Ross conjectured that an optimal policy is threshold in the posterior probability that the target is at site~1. MacPhee and Jordan proved the conjecture throughout the nonpositive-determinant ($\det M\le0$) regime and for part of the positive-determinant ($\det M>0$) regime, leaving the remaining cases open. We prove threshold optimality throughout the positive-determinant regime, completing Ross's conjecture for all parameter values.

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Yunpeng Li. 2026-09-03. A proof of Ross's conjecture for two-site moving-target search. https://arxiv.org/abs/2608.09368

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