Computing Minimal Unique Substrings for a Sliding Window
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Published:2021-08-20
Issue:
Volume:
Page:
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ISSN:0178-4617
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Container-title:Algorithmica
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language:en
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Short-container-title:Algorithmica
Author:
Mieno TakuyaORCID, Fujishige Yuta, Nakashima Yuto, Inenaga Shunsuke, Bannai Hideo, Takeda Masayuki
Abstract
AbstractA substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. In this paper, we study the problem of computing MUSs for a sliding window over a given string T. We first show how the set of MUSs can change when the window slides over T. We then present an $$O(n\log \sigma ')$$
O
(
n
log
σ
′
)
-time and O(d)-space algorithm to compute MUSs for a sliding window of size d over the input string T of length n, where $$\sigma '\le d$$
σ
′
≤
d
is the maximum number of distinct characters in every window.
Funder
Japan Society for the Promotion of Science Japan Science and Technology Agency
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,General Computer Science
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