Chasing puppies on orthogonal straight-line plane graphs

Assume that you have lost your puppy on an embedded graph. You can walk around on the graph and the puppy will run towards you at infinite speed, always locally minimizing the distance to your current position. Is it always possible for you to reunite with the puppy? We show that if the embedded graph is an orthogonal straight-line embedding the answer is yes.

Publication Details

Journal
ArXiv.org
Published
2025-03-07
Primary Topic
Computational Geometry and Mesh Generation
Type
article
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article

Chasing puppies on orthogonal straight-line plane graphs

ArXiv.org
Computational Geometry and Mesh Generation
article

Chasing puppies on orthogonal straight-line plane graphs

article en

Abstract

Assume that you have lost your puppy on an embedded graph. You can walk around on the graph and the puppy will run towards you at infinite speed, always locally minimizing the distance to your current position. Is it always possible for you to reunite with the puppy? We show that if the embedded graph is an orthogonal straight-line embedding the answer is yes.

ArXiv.org
Openalex Percentile: Top 33%
Computational Geometry and Mesh Generation
Open Access PDFOpenAlex
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Chasing puppies on orthogonal straight-line plane graphs · ArXiv.org (2025) | TGRS Research Map | TGRS