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- W4295197850 abstract "In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to node-labeled trees and graphs by replacing substring with connected subgraph. In this paper, we give an ${n^2}/{2^{Omega(log n/log log n)^{1/2}}}$ time solution for both strings and trees. This odd-looking time complexity improves the state of the art $O(n^2/log^2 n)$ solutions by more than any poly-logarithmic factor. It originates from the recent seminal algorithm of Williams for min-plus matrix multiplication. We obtain the result by giving a black box reduction from trees to strings. This is then combined with a reduction from strings to min-plus matrix multiplications." @default.
- W4295197850 created "2022-09-12" @default.
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- W4295197850 date "2014-01-09" @default.
- W4295197850 modified "2023-09-25" @default.
- W4295197850 title "Binary Jumbled Pattern Matching via All-Pairs Shortest Paths" @default.
- W4295197850 doi "https://doi.org/10.48550/arxiv.1401.2065" @default.
- W4295197850 hasPublicationYear "2014" @default.
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