Substring Range Reporting

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.