Induced permutations for approximate metric search

Permutation-based Indexing (PBI) approaches have been proven to be particularly effective for conducting large-scale approximate metric searching. These methods rely on the idea of transforming the original metric objects into permutation representations, which can be efficiently indexed using data structures such as inverted files. The standard conceptualization of permutation associated with a metric object involves only the use of object distances and their relative orders from a set of anchors called pivots. In this paper, we generalized this definition in order to enlarge the class of permutation representations that can be used by PBI approaches. In particular, we introduced the concept of permutation induced by a space transformation and a sorting function, and we investigated which properties these transformations should possess to produce permutations that are effective for metric search. Furthermore, as a practical outcome, we defined a new type of permutation representation that is calculated using distances from pairs of pivots. This proposed technique allowed us to produce longer permutations than traditional ones for the same number of object-pivot distance calculations. The advantage lies in the fact that when longer permutations are employed, the use of inverted files built on permutation prefixes leads to greater efficiency in the search phase.