Opportunistic data structures with applications

In this paper we address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space reduction is achieved at no significant slowdown in the query performance. More precisely, its space occupancy is optimal in an information-content sense because a text T[1, u] is stored using O(H_k(T))+o(1) bits per input symbol in the worst case, where H_k (T) is the kth order empirical entropy of T (the bound holds for any fixed k). Given an arbitrary string P[1,p], the opportunistic data structure allows to search for the occ occurrences of P in T in O(p+occ log^ε u) time (for any fixed ε>0). If data are uncompressible we achieve the best space bound currently known; on compressible data our solution improves the succinct suffix array of [12] and the classical suffix tree and suffix array data structures either in space or in query time or both. We also study our opportunistic data structure in a dynamic setting and devise a variant achieving effective search and update time bounds. Finally, we show how to plug our opportunistic data structure into the Glimpse tool. The result is an indexing tool which achieves sublinear space and sublinear query time complexity.