An improved lion strategy for the lion and man problem
This is an incremental improvement to a theoretical pursuit-evasion game, relevant for researchers in computational geometry or game theory.
The paper tackles the lion and man problem by proposing a novel lion strategy that updates the center at each move, improving upon Sgall's method, and proves convergence with an upper bound on game length that dominates existing bounds.
In this paper, a novel lion strategy for David Gale's lion and man problem is proposed. The devised approach enhances a popular strategy proposed by Sgall, which relies on the computation of a suitable "center". The key idea of the new strategy is to update the center at each move, instead of computing it once and for all at the beginning of the game. Convergence of the proposed lion strategy is proven and an upper bound on the game length is derived, which dominates the existing bounds.