Linear-time nearest point algorithms for coxeter lattices

  • Authors:
  • Robby G. McKilliam;Warren D. Smith;I. Vaughan L. Clarkson

  • Affiliations:
  • School of Information Technology and Electrical Engineering, The University of Queensland, Australia;Center for Range Voting, Stony Brook, NY;School of Information Technology and Electrical Engineering, The University of Queensland, Australia

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

The Coxeter lattices are a family of lattices containing many of the important lattices in lowdimensions. This includes An, E7, E8 and their duals An*, E7*, and E8*. 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(n log n) 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.