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In this work, we study the existence of crossing gates on non-uniform and weighted grids. We establish an equivalence between uniform weighted crossing gates and a class of simple non-uniform crossing gates, which we call primal. We also exhibit a crossing gate that inherently requires more than one crossing, rather than a single crossing as in standard constructions. Finally, we show that the equivalence between uniform weighted and primal crossings breaks down in more general settings.
From: Pablo Concha-Vega [view email]
[v1]
Thu, 25 Jun 2026 12:17:09 UTC (30 KB)
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