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

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

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Author Details

Nil Mamano
  • Department of Computer Science, University of California, Irvine, USA
Alon Efrat
  • Department of Computer Science, University of Arizona, Tucson, USA
David Eppstein
  • Department of Computer Science, University of California, Irvine, USA
Daniel Frishberg
  • Department of Computer Science, University of California, Irvine, USA
Michael T. Goodrich
  • Department of Computer Science, University of California, Irvine, USA
Stephen Kobourov
  • Department of Computer Science, University of Arizona, Tucson, USA
Pedro Matias
  • Department of Computer Science, University of California, Irvine, USA
Valentin Polishchuk
  • Communications and Transport Systems, ITN, Linköping University, Sweden

Funding

  • Eppstein, David: Supported in part by NSF grants CCF-1618301 and CCF-1616248.
  • Goodrich, Michael T.: Supported in part by NSF grant 1815073.
  • Kobourov, Stephen: Supported in part by NSF grants CCF-1740858, CCF-1712119, DMS-1839274, and DMS-1839307.

Cite As Get BibTex

Nil Mamano, Alon Efrat, David Eppstein, Daniel Frishberg, Michael T. Goodrich, Stephen Kobourov, Pedro Matias, and Valentin Polishchuk. New Applications of Nearest-Neighbor Chains: Euclidean TSP and Motorcycle Graphs. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.51

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Computational geometry
Keywords
  • Nearest-neighbors
  • Nearest-neighbor chain
  • motorcycle graph
  • straight skeleton
  • multi-fragment algorithm
  • Euclidean TSP
  • Steiner TSP

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