Euclidean TSP, motorcycle graphs, and other new applications of nearest-neighbor chains

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

Research output: Contribution to journalArticlepeer-review

Abstract

We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: We 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 p n log n) time; we compute motorcycle graphs (which are a central part in straight skeleton algorithms) in O(n4/3+ϵ) time for any ϵ0; we introduce a narcissistic variant of the k-attribute stable matching model, and solve it in O(n2-4/(k(1+ϵ)+2)) time; we give a linear-time 2-approximation for a 1D geometric set cover problem with applications to radio station placement.

MSC Codes I.3.5

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Feb 18 2019

Keywords

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

ASJC Scopus subject areas

  • General

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