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

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

Computer Science

Research output: Contribution to journal › Article › peer-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 language	English (US)
Journal	Unknown Journal
State	Published - 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

Fingerprint Dive into the research topics of 'Euclidean TSP, motorcycle graphs, and other new applications of nearest-neighbor chains'. Together they form a unique fingerprint.

Cite this

@article{f7ff42b6d0914c91abe38b2ee2e3b04e,

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

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",

keywords = "Euclidean TSP, Motorcycle graph, Multi-fragment algorithm, Nearest-neighbor chain, Nearest-neighbors, Steiner TSP, Straight skeleton, Succinct stable matching",

author = "Nil Mamano and Alon Efrat and David Eppstein and Daniel Frishberg and Goodrich, {Michael T.} and Stephen Kobourov and Pedro Matias and Valentin Polishchuk",

year = "2019",

month = feb,

day = "18",

language = "English (US)",

journal = "Nuclear Physics A",

issn = "0375-9474",

publisher = "Elsevier",

}

TY - JOUR

T1 - Euclidean TSP, motorcycle graphs, and other new applications of nearest-neighbor chains

AU - Mamano, Nil

AU - Efrat, Alon

AU - Eppstein, David

AU - Frishberg, Daniel

AU - Goodrich, Michael T.

AU - Kobourov, Stephen

AU - Matias, Pedro

AU - Polishchuk, Valentin

PY - 2019/2/18

Y1 - 2019/2/18

N2 - 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

AB - 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

KW - Euclidean TSP

KW - Motorcycle graph

KW - Multi-fragment algorithm

KW - Nearest-neighbor chain

KW - Nearest-neighbors

KW - Steiner TSP

KW - Straight skeleton

KW - Succinct stable matching

UR - http://www.scopus.com/inward/record.url?scp=85094693238&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85094693238&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85094693238

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -