2011/08/18 by Philip Bille, Bille, Philip, Inge Li Goertz +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Network Packet Processing and Optimization #cs.DS
paper · pdf · doi:10.48550/arxiv.1108.3683
arxiv created 2011/08/18 · openalex publication_date 2011/08/18 · arxiv updated 2011/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results. itemize We give efficient reductions for each of the above problems to a new problem, which we call substring range reporting. Hence, we unify the previous work by showing that we may restrict our attention to a single problem rather than studying each of the above problems individually. We show how to solve substring range reporting with optimal query time and little space. Combined with our reductions this leads to significantly improved time-space trade-offs for the above problems. In particular, for each problem we obtain the first solutions with optimal time query and O(nlogO(1) n) space, where n is the length of the indexed string. We show that our techniques for substring range reporting generalize to substring range counting and substring range emptiness variants. We also obtain non-trivial time-space trade-offs for these problems. itemize Our bounds for substring range reporting are based on a novel combination of suffix trees and range reporting data structures. The reductions are simple and general and may apply to other combinations of string indexing with range reporting.