Abstract
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.
| Original language | English |
|---|---|
| Title of host publication | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |
| Editors | Anca Muscholl, Piotr Faliszewski, Rolf Niedermeier |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959770163 |
| DOIs | |
| Publication status | Published - Aug 1 2016 |
| Event | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland Duration: Aug 22 2016 → Aug 26 2016 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 58 |
| ISSN (Print) | 1868-8969 |
Other
| Other | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |
|---|---|
| Country | Poland |
| City | Krakow |
| Period | 8/22/16 → 8/26/16 |
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All Science Journal Classification (ASJC) codes
- Software
Cite this
Computing DAWGs and minimal absent words in linear time for integer alphabets. / Fujishige, Yuta; Tsujimaru, Yuki; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.
41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016. ed. / Anca Muscholl; Piotr Faliszewski; Rolf Niedermeier. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016. 38 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 58).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
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
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
ER -