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arXiv · 1210.8386

Grammar-Based Construction of Indexes for Binary Jumbled Pattern Matching

Travis Gagie
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Abstract

We show how, given a straight-line program with $g$ rules for a binary string $B$ of length $n$, in $O(g^{2 / 3} n^{4 / 3})$ time we can build a linear-space index such that, given $m$ and $c$, in O(1) time we can determine whether there is a substring of $B$ with length $m$ containing exactly $c$ copies of 1. If we use $O(n \log n)$ space for the index, then we can list all such substrings using $O(m)$ time per substring.

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Travis Gagie. 2012-11-15. Grammar-Based Construction of Indexes for Binary Jumbled Pattern Matching. https://arxiv.org/abs/1210.8386

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