On Generalizing Permutation-Based Representations for Approximate Search

In the domain of approximate metric search, the Permutation-based Indexing (PBI) approaches have been proved to be particularly suitable for dealing with large data collections. 
These methods employ a permutation-based representation of the data, which can be efficiently indexed using data structures such as inverted files. In the literature, the definition of the permutation of a metric object was derived by reordering the distances of the object to a set of pivots. In this paper, we aim at generalizing this definition 
in order to enlarge the class of permutations that can be used by PBI approaches. As a practical outcome, we defined a new type of permutation that is calculated using distances from pairs of pivots. The proposed technique permits us to produce longer permutations than traditional ones for the same number of object-pivot distance calculations. The advantage is that the use of inverted files built on permutation prefixes leads to greater efficiency in the search phase when longer permutations are used.