TY - GEN

T1 - Computing DAWGs and minimal absent words in linear time for integer alphabets

AU - Fujishige, Yuta

AU - Tsujimaru, Yuki

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

N1 - Publisher Copyright:
© Peter Fulla and Stanislav Živný.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2016/8/1

Y1 - 2016/8/1

N2 - The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the first O(n)-time algorithm for constructing the affix tree of a given string y over an integer alphabet. Affix trees are a text indexing structure supporting bidirectional pattern searches. As an application to our O(n)-time DAWG construction algorithm, we show that the set MAW(y) of all minimal absent words of y can be computed in optimal O(n +MAW(y)) time and O(n) working space for integer alphabets.

AB - The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the first O(n)-time algorithm for constructing the affix tree of a given string y over an integer alphabet. Affix trees are a text indexing structure supporting bidirectional pattern searches. As an application to our O(n)-time DAWG construction algorithm, we show that the set MAW(y) of all minimal absent words of y can be computed in optimal O(n +MAW(y)) time and O(n) working space for integer alphabets.

UR - http://www.scopus.com/inward/record.url?scp=85012877585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012877585&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2016.38

DO - 10.4230/LIPIcs.MFCS.2016.38

M3 - Conference contribution

AN - SCOPUS:85012877585

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

A2 - Muscholl, Anca

A2 - Faliszewski, Piotr

A2 - Niedermeier, Rolf

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

Y2 - 22 August 2016 through 26 August 2016

ER -