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.ISAAC.2019.51
URN: urn:nbn:de:0030-drops-115477
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11547/
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Mamano, Nil ; Efrat, Alon ; Eppstein, David ; Frishberg, Daniel ; Goodrich, Michael T. ; Kobourov, Stephen ; Matias, Pedro ; Polishchuk, Valentin

New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs

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LIPIcs-ISAAC-2019-51.pdf (0.7 MB)

Abstract

We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We use it to construct the greedy multi-fragment tour for Euclidean TSP in O(n log n) time in any fixed dimension and for Steiner TSP in planar graphs in O(n sqrt(n)log n) time; we compute motorcycle graphs, a central step in straight skeleton algorithms, in O(n^(4/3+epsilon)) time for any epsilon>0.

BibTeX - Entry

@InProceedings{mamano_et_al:LIPIcs:2019:11547,
  author =	{Nil Mamano and Alon Efrat and David Eppstein and Daniel Frishberg and Michael T. Goodrich and Stephen Kobourov and Pedro Matias and Valentin Polishchuk},
  title =	{{New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11547},
  URN =		{urn:nbn:de:0030-drops-115477},
  doi =		{10.4230/LIPIcs.ISAAC.2019.51},
  annote =	{Keywords: Nearest-neighbors, Nearest-neighbor chain, motorcycle graph, straight skeleton, multi-fragment algorithm, Euclidean TSP, Steiner TSP}
}

Keywords: Nearest-neighbors, Nearest-neighbor chain, motorcycle graph, straight skeleton, multi-fragment algorithm, Euclidean TSP, Steiner TSP
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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