Optimal Trees for Searching in Codebook

Finding nearest neighbour of a given vector in a codebook leads to the following model of searching. In a metric space V, a vector x and a finite subset of vectors S (representing a codebook) are given. We have to find an element of S which is ,,nearest" to the element x. In what follows, the problem is formulated more exactly and a characterization of optimal search trees for this model of searching is given. It turns out, that balanced quasi-ternary trees are optimal search trees for the discussed problem. The result enables to speed up finding a codebook representation vector of a given acoustic vector, which is important for applications in speech recognition and synthesis