Substring Range Reporting

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.

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(nlog O(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.

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.
Original languageEnglish
JournalAlgorithmica
Volume69
Issue number2
Pages (from-to)384-396
ISSN0178-4617
DOIs
Publication statusPublished - 2014

Keywords

  • String indexing
  • Range reporting
  • Gaps
  • Position-restricted substring searching

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