Indexing weighted sequences: Neat and efficient

A weighted sequence is a sequence of probability mass functions over a finite alphabet. A weighted index is a data structure constructed for a weighted sequence and a threshold 1z that, given a string pattern, reports all positions where it occurs in the weighted sequence with probability at least 1z. We present an O(nz)-time construction of an O(nz)-sized weighted index for a weighted sequence of length n that answers queries in optimal time. The previous solution by Amir et al. (2008) required O(nz2log⁡z) time and space. Our main tools are a construction of a family of ⌊z⌋ strings that carries the information about all the strings that occur in a weighted sequence and a more straightforward solution to so-called property indexing. We present applications of our weighted index, in particular in approximate and general scenarios that were introduced by Biswas et al. (2016), and provide its implementation.