Faster subsequence recognition in compressed strings (0707.3407v4)

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 $\bar m$, and an uncompressed pattern of length $n$, C{\'e}gielski et al. gave an algorithm for local subsequence recognition running in time $O(\bar mn^2 \log n)$. We improve the running time to $O(\bar mn^{1.5})$. Our algorithm can also be used to compute the longest common subsequence between a compressed text and an uncompressed pattern in time $O(\bar mn^{1.5})$; the same problem with a compressed pattern is known to be NP-hard.