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.
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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 -