Computing the longest unbordered substring

Paweł Gawrychowski, Gregory Kucherov, Benjamin Sach, Tatiana Starikovskaya

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Citations (Scopus)


A substring of a string is unbordered if its only border is the empty string. The study of unbordered substrings goes back to the paper of Ehrenfeucht and Silberger [Discr. Math 26 (1979)]. The main focus of their and subsequent papers was to elucidate the relationship between the longest unbordered substring and the minimal period of strings. In this paper, we consider the algorithmic problem of computing the longest unbordered substring of a string. The problem was introduced recently by G. Kucherov et al. [CPM (2015)], where the authors showed that the average-case running time of the simple, border-array based algorithm can be bounded by O(max{n, n24}) for σ being the size of the alphabet. (The worst-case running time remained O(n2).) Here we propose two algorithms, both presenting substantial theoretical improvements to the result of [11]. The first algorithm has O(n log n) average-case running time and O(n2) worst-case running time, and the second algorithm has O(n1.5) worst-case running time.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings
EditorsSimon J. Puglisi, Costas S. Iliopoulos, Emine Yilmaz
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319238258
Publication statusPublished - 2015
Externally publishedYes
Event22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015 - London, United Kingdom
Duration: 1 Sep 20154 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015
Country/TerritoryUnited Kingdom


Dive into the research topics of 'Computing the longest unbordered substring'. Together they form a unique fingerprint.

Cite this