License:
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.45
URN: urn:nbn:de:0030-drops-75949
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7594/
Frieze, Alan ;
Pegden, Wesley
Traveling in Randomly Embedded Random Graphs
Abstract
We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a geodesic of length arbitrarily close to their Euclidean distance, and analyze the minimum length Traveling Salesperson Tour, extending the Beardwood-Halton-Hammersley theorem to this setting.
BibTeX - Entry
@InProceedings{frieze_et_al:LIPIcs:2017:7594,
author = {Alan Frieze and Wesley Pegden},
title = {{Traveling in Randomly Embedded Random Graphs}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
pages = {45:1--45:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-044-6},
ISSN = {1868-8969},
year = {2017},
volume = {81},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7594},
URN = {urn:nbn:de:0030-drops-75949},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.45},
annote = {Keywords: Traveling Salesman, Euclidean, Shortest Path}
}
Keywords: |
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Traveling Salesman, Euclidean, Shortest Path |
Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) |
Issue Date: |
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2017 |
Date of publication: |
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11.08.2017 |