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- W4301379968 abstract "Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d geq 2$ of the documents. This problem is known as the emph{longest common substring (LCS) problem} and has a classic $O(n)$ space and $O(n)$ time solution (Weiner [FOCS'73], Hui [CPM'92]). However, the use of linear space is impractical in many applications. In this paper we show that for any trade-off parameter $1 leq tau leq n$, the LCS problem can be solved in $O(tau)$ space and $O(n^2/tau)$ time, thus providing the first smooth deterministic time-space trade-off from constant to linear space. The result uses a new and very simple algorithm, which computes a $tau$-additive approximation to the LCS in $O(n^2/tau)$ time and $O(1)$ space. We also show a time-space trade-off lower bound for deterministic branching programs, which implies that any deterministic RAM algorithm solving the LCS problem on documents from a sufficiently large alphabet in $O(tau)$ space must use $Omega(nsqrt{log(n/(taulog n))/loglog(n/(taulog n)})$ time." @default.
- W4301379968 created "2022-10-05" @default.
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- W4301379968 date "2014-07-02" @default.
- W4301379968 modified "2023-09-28" @default.
- W4301379968 title "Sublinear Space Algorithms for the Longest Common Substring Problem" @default.
- W4301379968 doi "https://doi.org/10.48550/arxiv.1407.0522" @default.
- W4301379968 hasPublicationYear "2014" @default.
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