Abstract
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to Lempel–Ziv compression. For an SLP-compressed text of length $\overline{m}$ , and an uncompressed pattern of length n, Cegielski et al. gave an algorithm for local subsequence recognition running in time $O\left( {\overline{m} n^2 \log n}\right)$. We improve the running time to $O\left( {\overline{m} n^{1.5} }\right)$. Our algorithm can also be used to compute the longest common subsequence between a compressed text and an uncompressed pattern in time $O\left( {\overline{m} n^{1.5} }\right)$; the same problem with a compressed pattern is known to be NP-hard.
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