New applications of nearest-neighbor chains: Euclidean TSP and motorcycle graphs

Nil Mamano, David Eppstein, Michael T. Goodrich, Pedro Matias, Alon Efrat, Daniel Frishberg, Stephen Kobourov, Valentin Polishchuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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√n log n) time; we compute motorcycle graphs, a central step in straight skeleton algorithms, in O(n4/3+ε) time for any ε > 0.

Original languageEnglish (US)
Title of host publication30th International Symposium on Algorithms and Computation, ISAAC 2019
EditorsPinyan Lu, Guochuan Zhang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771306
DOIs
StatePublished - Dec 2019
Event30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China
Duration: Dec 8 2019Dec 11 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume149
ISSN (Print)1868-8969

Conference

Conference30th International Symposium on Algorithms and Computation, ISAAC 2019
CountryChina
CityShanghai
Period12/8/1912/11/19

Keywords

  • Euclidean TSP
  • Motorcycle graph
  • Multi-fragment algorithm
  • Nearest-neighbor chain
  • Nearest-neighbors
  • Steiner TSP
  • Straight skeleton

ASJC Scopus subject areas

  • Software

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  • Cite this

    Mamano, N., Eppstein, D., Goodrich, M. T., Matias, P., Efrat, A., Frishberg, D., Kobourov, S., & Polishchuk, V. (2019). New applications of nearest-neighbor chains: Euclidean TSP and motorcycle graphs. In P. Lu, & G. Zhang (Eds.), 30th International Symposium on Algorithms and Computation, ISAAC 2019 [51] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 149). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2019.51