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.
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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.
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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.
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.
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Bille, P., Gørtz, I.L. (2011). Substring Range Reporting. In: Giancarlo, R., Manzini, G. (eds) Combinatorial Pattern Matching. CPM 2011. Lecture Notes in Computer Science, vol 6661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21458-5_26
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DOI: https://doi.org/10.1007/978-3-642-21458-5_26
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