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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 aarXiv:1902.06875v3 fatcat:irn2mhfvr5futge4dtzraidesi