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  "path": "/abs/2603.09750v1",
  "publishedAt": "2026-03-11T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Stephen Kobourov",
    "William Lenhart",
    "Giuseppe Liotta",
    "Daniel Perz",
    "Pavel Valtr",
    "Johannes Zink"
  ],
  "textContent": "**Authors:** Stephen Kobourov, William Lenhart, Giuseppe Liotta, Daniel Perz, Pavel Valtr, Johannes Zink\n\nWe 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.",
  "title": "Simultaneous Embedding of Two Paths on the Grid"
}