Abstract
The classical and extensively-studied Fréchet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a “flipped” Fréchet measure defined by a sup min - the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of “social distance” between two curves (or general domains), where agents traverse curves while trying to stay as far apart as possible. We first study the flipped Fréchet measure between two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms. We then consider this measure on polygons, where it denotes the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon. We investigate several variants of the problem in this setting, for some of which we provide linear time algorithms. Finally, we consider this measure on graphs. We draw connections between our proposed flipped Fréchet measure and existing related work in computational geometry, hoping that our new measure may spawn investigations akin to those performed for the Fréchet distance, and into further interesting problems that arise.
Original language | English |
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Title of host publication | 14th Innovations in Theoretical Computer Science Conference, ITCS 2023 |
Editors | Yael Tauman Kalai |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Pages | 51:1-51:22 |
Number of pages | 22 |
ISBN (Electronic) | 9783959772631 |
DOIs | |
State | Published - 1 Jan 2023 |
Event | 14th Innovations in Theoretical Computer Science Conference, ITCS 2023 - Cambridge, United States Duration: 10 Jan 2023 → 13 Jan 2023 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 251 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 14th Innovations in Theoretical Computer Science Conference, ITCS 2023 |
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Country/Territory | United States |
City | Cambridge |
Period | 10/01/23 → 13/01/23 |
Bibliographical note
Publisher Copyright:© Omrit Filtser, Mayank Goswami, Joseph S. B. Mitchell, and Valentin Polishchuk; licensed under Creative Commons License CC-BY 4.0.
Keywords
- curves
- distancing measure
- polygons