Some approaches to best-match file searching

Abstract

The problem of searching the set of keys in a file to find a key which is closest to a given query key is discussed. After “closest,” in terms of a metric on the the key space, is suitably defined, three file structures are presented together with their corresponding search algorithms, which are intended to reduce the number of comparisons required to achieve the desired result. These methods are derived using certain inequalities satisfied by metrics and by graph-theoretic concepts. Some empirical results are presented which compare the efficiency of the methods.

t-Spanners for metric space searching

“…Among them we can find structures for discrete or continuous distance functions. In the discrete case we have: Burkhard-Keller Tree (BKT) [10], Fixed Queries Tree (FQT) [4], Fixed-Height FQT (FHQT) [4,3], and Fixed Queries Array (FQA) [14]. In the continuous case we have: Vantage-Point Tree (VPT) [42,17,39], Multi-Vantage-Point Tree (MVPT) [9,8], Excluded Middle Vantage Point Forest (VPF) [43], Approximating Eliminating Search Algorithm (AESA) [40], and Linear AESA (LAESA) [29].…”

Indexing Issues in Supporting Similarity Searching

“…We use the term distance-based indexing to describe such methods (e.g., [9]). A number of such methods have been proposed over the past few decades, some of the earliest being due to Burkhard and Keller [10]. These methods generally assume that we are given a finite set S of N objects and a distance metric d indicating the distance values between them (collectively termed a finite metric space) Typical of distance-based indexing structures are metric trees [11,12], which are binary trees that result in recursively partitioning a data set into two subsets at each node.…”

Similarity search without tears: the OMNI-family of all-purpose access methods

“…The seminal work of Burkhard and Keller [9] provides different interesting techniques for partitioning a metric data set where the recursive process is materialized as a tree. The first technique partitions a dataset by choosing a representative from the set and grouping the elements with respect to their distance from it.…”

“…The representative and the maximum distance from the representative to a point of the corresponding subset are also maintained to support nearest neighbor queries. The metric tree of Uhlmann [20] and the vantage-point tree (vp-tree) of Yanilos [23] are somehow similar to the first technique of [9] as they partition the elements into two groups according to a representative, called a vantage point. In [23] the vp-tree has been generalized to a multi-way tree.…”