























It was recently proved that any SLP generating a given string $w$ can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We show that this result also holds for RLSLPs, which are SLPs extended with run-length rules of the form $A \rightarrow B^t$ for $t>2$, deriving $\texttt{exp}(A) = \texttt{exp}(B)^t$. An immediate consequence is the simplification of the algorithm for extracting substrings of an RLSLP-compressed string. We also show that several problems like answering RMQs and computing Karp-Rabin fingerprints on substrings can be solved in $\mathcal{O}(g_{rl})$ space and $\mathcal{O}(\log n)$ time, $g_{rl}$ being the size of the smallest RLSLP generating the string, of length $n$. We extend the result to solving more general operations on string ranges, in $\mathcal{O}(g_{rl})$ space and $\mathcal{O}(\log n)$ applications of the operation. In general, the smallest RLSLP can be asymptotically smaller than the smallest SLP by up to an $\mathcal{O}(\log n)$ factor, so our results can make a difference in terms of the space needed for computing these operations efficiently for some string families.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。