← 研踪 PaperTrailarXiv:2610.38114 · v1
Output-Sensitive Enumeration of Maximal Closed Substrings in Linear Space
首次提交 2026-10-28 08:50
版本更新 2026-10-28 08:50
雷达观测 2026-10-30 10:23
摘要
We revisit the output-sensitive enumeration of maximal closed substrings (MCSs). Given a string of length $n$ over an integer alphabet, let $k$ denote its number of MCS occurrences. We combine a right-to-left sweep on the string with range-successor queries to obtain all MCSs with two deterministic word-RAM bounds: for any fixed $\varepsilon>0$, we can report all MCSs in $O(n\sqrt{\log n}+k\log^\varepsilon n)$ time using $O(n)$ words of space, or in $O(n\sqrt{\log n}+k\log\log n)$ time using $O(n\log\log n)$ words. Both bounds include preprocessing and report occurrences by their endpoints. In particular, these algorithms improve the known $O(n\log n)$ worst-case time bound for sufficiently small output.
观测到的版本
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v1 · 2026-10-28 08:50 · 最新观测版本
Output-Sensitive Enumeration of Maximal Closed Substrings in Linear Space
We revisit the output-sensitive enumeration of maximal closed substrings (MCSs). Given a string of length $n$ over an integer alphabet, let $k$ denote its number of MCS occurrences. We combine a right-to-left sweep on the string with range-successor queries to obtain all MCSs with two deterministic word-RAM bounds: for any fixed $\varepsilon>0$, we can report all MCSs in $O(n\sqrt{\log n}+k\log^\varepsilon n)$ time using $O(n)$ words of space, or in $O(n\sqrt{\log n}+k\log\log n)$ time using $O(n\log\log n)$ words. Both bounds include preprocessing and report occurrences by their endpoints. In particular, these algorithms improve the known $O(n\log n)$ worst-case time bound for sufficiently small output.
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