Abstract
We introduce efficient data structures for an indexing problem in non-standard stringology — jumbled pattern matching. Moosa and Rahman [J. Discr. Alg., 2012] gave an index for jumbled pattern matching for the case of binary alphabets with \(O(\frac{n^2}{\log^2 n})\)-time construction. They posed as an open problem an efficient solution for larger alphabets. In this paper we provide an index for any constant-sized alphabet. We obtain the first o(n 2)-space construction of an index with o(n) query time. It can be built in O(n 2) time. Precisely, our data structure can be implemented with O(n 2 − δ) space and O(m (2σ − 1)δ) query time for any δ > 0, where m is the length of the pattern and σ is the alphabet size (σ = O(1)). We also break the barrier of quadratic construction time for non-binary constant alphabet simultaneously obtaining poly-logarithmic query time.
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Kociumaka, T., Radoszewski, J., Rytter, W. (2013). Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_53
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DOI: https://doi.org/10.1007/978-3-642-40450-4_53
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