New formulation and improvements of the nearest-neighbour approximating and eliminating search algorithm (AESA)

Abstract

Recently, the Approximating and Eliminating Search Algorithm (AESA) was introduced to search for Nearest Neighbours in asymptotically constant average time complexity. In this paper, a new development of the AESA is presented which formally adheres to the general algorithmic strategy of (best-first) Branch and Bound (B&B). This development naturally suggests a new selection or Approximating Criterion which: (a) is cheaper to compute, (b) significantly reduces the “overhead” or computation not alloted to distance computation, (c) leads to a more compact and clear presentation of the AESA, and (d) slightly but consistently reduces the average number of required distance computations. Experimental evidence assessing the last mentioned improvement is presented.