5 research outputs found
Optimal Prefix and Suffix Queries on Texts
International audienceIn this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied by Makinen and Navarro [V. Makinen, G. Navarro, Position-restricted substring searching, in: J.R. Correa, A. Hevia, M.A. Kiwi (Eds.), LATIN, in: Lecture Notes in Computer Science, vol. 3887, Springer, 2006, pp. 703-714]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by Makinen and Navarro, if applied to our problem, gives sub-optimal query time and the corresponding data structure also requires more time and space
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.
{itemize} We give efficient reductions for each of the above problems to a new
problem, which we call \emph{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 space,
where is the length of the indexed string. We show that our techniques for
substring range reporting generalize to \emph{substring range counting} and
\emph{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
Optimal Prefix and Suffix Queries on Texts
Abstract. In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied MĂ€kinen and Navarro [Position-Restricted Substring Searching, LATIN 2006]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by MĂ€kinen and Navarro, if applied to our problem, gives sub-optimal query time and the corresponding data structure also requires more time and space.
Optimal Prefix and Suffix Queries on Texts
In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied by MĂ€kinen and Navarro [Position-Restricted Substring Searching, LATIN 2006]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by MĂ€kinen and Navarro, if applied to our problem, gives sub-optimal query time and the corresponding data structure also requires more time and space