Revisit escape path for infinite unit strip forest and unit broadworm

Zhipeng Deng

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arXiv · 2607.18563

Revisit escape path for infinite unit strip forest and unit broadworm

Zhipeng Deng

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Abstract

Building on our previous general computational solution to Bellman's Lost-in-a-Forest Problem, we present a new approach and analytical formulas for the previously well-known escape path for the infinite unit-strip forest and unit broadworm by Zalgaller. Earlier studies addressed these problems exclusively through geometric methods. We reformulated the problem as an interval-cover problem and then formulated it as a constrained functional minimization problem. This constrained functional minimization can be directly discretized and subsequently solved as a convex optimization. Furthermore, we extend the analysis of various line segment. Finally, we show that, in the case of a closed escape path for the unit strip, the optimal solution is a curve of constant unit width.

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Zhipeng Deng. 2026-07-20. Revisit escape path for infinite unit strip forest and unit broadworm. https://arxiv.org/abs/2607.18563

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