Accessing the Suffix Array via ϕ-1-Forest

Kärkkainen et al. (CPM, 2009) defined the concept of ϕ that later became key to the construction of the r -index. Given a string S [1.. n ], its suffix array SA and its inverse suffix array ISA , we define ϕ as the permutation of { 1 , … , n } such that ϕ ( i ) = SA [ ISA [ i ] - 1 ] if ISA [ i ] > 1 , and ϕ ( i ) = SA [ n ] otherwise. Gagie et al. (JACM, 2020) showed that it is possible to store O ( r ) words such that the permutations ϕ and ϕ - 1 are evaluated in O ( log log w ( n / r ) ) -time, which was improved to O ( 1 ) -time by Nishimoto and Tabei (ICALP, 2021). In this paper, we introduce the concept of ϕ - 1 -forest, which is a data structure using sampled SA values to speed up random access to SA . We implemented our approach and compared its performance with respect to the r -index.