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arXiv · 2603.09750

Simultaneous Embedding of Two Paths on the Grid

Stephen Kobourov·William Lenhart·Giuseppe Liotta·Daniel Perz·Pavel Valtr·Johannes Zink
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Abstract

We study the problem of simultaneous geometric embedding of two paths without self-intersections on an integer grid. We show that minimizing the length of the longest edge of such an embedding is NP-hard. We also show that we can minimize in $O(n^{3/2})$ time the perimeter of an integer grid containing such an embedding if one path is $x$-monotone and the other is $y$-monotone.

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Stephen Kobourov, William Lenhart, Giuseppe Liotta, Daniel Perz, Pavel Valtr, Johannes Zink. 2026-03-10. Simultaneous Embedding of Two Paths on the Grid. https://arxiv.org/abs/2603.09750

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