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The Coxeter lattices are a family of lattices containing many of the important lattices in low dimensions. This includes An, E 7 , E 8 and their duals An*, E 7*, and E 8*. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity O(nlogn) and the other with worst case complexity O(n) where n is the dimension of the lattice. We show that for the particular lattices An and An* the algorithms are equivalent to nearest point algorithms that already exist in the literature.

Linear-Time Nearest Point Algorithms for Coxeter Lattices