Author

A. Temerev

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Preprint Sep 2026

The logarithmic spiral is optimal for shoreline search: a computer-assisted proof

A ship starts at a point of the plane and moves at unit speed; it has to reach an unknown straight line, of which neither the distance nor the direction is known. The competitive ratio of a path is the supremum, over all lines, of the time at which the line is reached divided by its distance. Baeza-Yates, Culberson and...

A. Temerev · 1 citation

Preprint Aug 2026

A new unconditional lower bound for shoreline search

A unit-speed searcher starts at the origin of the Euclidean plane and must hit an unknown straight line whose direction and distance from the origin are both unknown. We prove that every deterministic search path has competitive ratio at least $C_{\log}\approx 12.5937096701246675$. The bound is unconditional: the path...

A. Temerev · 3 citations