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Two robots moving
geodesically on a tree
Donald M Davis, Michael Harrison and David Recio-Mitter |
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Algebraic & Geometric Topology 22 (2022) 785–814
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Abstract |
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We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the and metrics. We determine the geodesic complexity of the ordered two-point –configuration space of any star graph in both the and metrics and of the unordered two-point configuration space of any tree in the metric, by finding explicit geodesics from any pair to any other pair, and arranging them into a minimal number of continuously varying families. In each case the geodesic complexity matches the known value of the topological complexity. |
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Keywords
geodesic, configuration space, topological robotics, graphs
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Mathematical Subject Classification
Primary: 53C22, 55M30, 55R80
Secondary: 68T40
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References |
Publication
Received: 2 July 2020
Revised: 8 December 2020
Accepted: 11 January 2021
Published: 3 August 2022
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Authors |
| Donald M Davis | |
| Department of Mathematics Lehigh University Bethlehem, PA United States |
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| Michael Harrison | |
| Institute for Advanced Study Princeton, NJ United States |
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| David Recio-Mitter | |
| Department of Mathematics Lehigh University Bethlehem, PA United States |
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