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arXiv · 2610.29994

Pinch-Free Orientations of Polyomino Grid Graphs

James Fox·Mirela Damian
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Abstract

We study lattice-based collective construction of a target polyomino on the integer grid, where robots place unit square blocks subject to two physical constraints: the partial structure must remain connected at all times, and no placement may create an unfillable one-cell gap. We present a wavefront sweep algorithm that computes a dependency structure satisfying the local conditions required for safe assembly. Given a list of n cells sorted lexicographically by coordinates, the orientation can be computed in O(n) time using O(n) auxiliary space.

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James Fox, Mirela Damian. 2026-10-21. Pinch-Free Orientations of Polyomino Grid Graphs. https://arxiv.org/abs/2610.29994

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