TL;DR
This paper investigates the optimal strategies for a group of travelers with bicycles aiming to minimize journey time, characterizing solutions using Dyck language and analyzing special cases with desirable properties.
Contribution
It introduces a novel characterization of optimal solutions to the Biker-hiker problem using Dyck language and explores solutions with additional properties.
Findings
Optimal solutions are characterized by Dyck words.
Certain solutions with desirable properties are identified and analyzed.
The problem's structure allows for combinatorial characterization.
Abstract
There are n travellers who have k bicycles and they wish to complete a journey in the shortest possible time. We investigate optimal solutions of this problem, showing they are characterized by a set of words in the Dyck language. Particular solutions with additional desirable properties are introduced and analysed.
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