The First Subquadratic Algorithm for Complete Linkage Clustering

Complete-linkage clustering is a very popular method for computing hierarchical clusterings in practice, which is not fully understood theoretically. Given a finite set $$P\subseteq \mathbb {R}^d$$P⊆Rd of points, the complete-linkage method starts with ...

In the 3SUM problem we are given three lists $$\mathcal {A}$$A, $$\mathcal {B}$$B, $$\mathcal {C}$$C, of n real numbers, and are asked to find $$(a,b,c)\in \mathcal {A}\times \mathcal {B}\times \mathcal {C}$$(a,b,c)źA B C such that $$a+b=c$$a+b=c. The ...

We obtain subquadratic algorithms for 3SUM on integers and rationals in several models. On a standard word RAM with w-bit words, we obtain a running time of $O(n^{2}/\max\{\frac{w}{\lg^{2}w},\frac{\lg^{2}n}{(\lg\lg n)^{2}}\})$ . In the circuit RAM with ...