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arXiv · 1902.06875

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

Nil Mamano·Alon Efrat·David Eppstein·Daniel Frishberg·Michael Goodrich·Stephen Kobourov·Pedro Matias·Valentin Polishchuk
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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 $O(n\sqrt{n}\log n)$ time; we compute motorcycle graphs (which are a central part in straight skeleton algorithms) in $O(n^{4/3+\varepsilon})$ time for any $\varepsilon>0$; we introduce a narcissistic variant of the $k$-attribute stable matching model, and solve it in $O(n^{2-4/(k(1+\varepsilon)+2)})$ time; we give a linear-time $2$-approximation for a 1D geometric set cover problem with applications to radio station placement.

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Nil Mamano, Alon Efrat, David Eppstein, Daniel Frishberg, Michael Goodrich, Stephen Kobourov, Pedro Matias, Valentin Polishchuk. 2019-02-19. Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor Chains. https://arxiv.org/abs/1902.06875

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