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

Nil Mamano, Alon Efrat, David Eppstein, Daniel Frishberg, Michael Goodrich, Stephen Kobourov, Pedro Matias, Valentin Polishchuk
2019 arXiv   pre-print
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(nlog n) time in any fixed dimension and for Steiner TSP in planar graphs in O(n√(n)log n) time; we compute motorcycle graphs (which are a central part in straight skeleton algorithms) in O(n^4/3+ε) time for any ε>0; we introduce a
more » ... variant of the k-attribute stable matching model, and solve it in O(n^2-4/(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.
arXiv:1902.06875v3 fatcat:irn2mhfvr5futge4dtzraidesi