# directed acyclic word graph

(data structure)

**Definition:**
(1) A *directed acyclic graph* representing the *suffixes* of a given *string* in which each *edge* is labeled with a character. The characters along a *path* from the *root* to a *node* are the *substring* which the *node* represents. (2) A *finite state machine* that recognizes a set of words.

**Also known as** DAWG.

**See also**
*compact DAWG*, *suffix tree*, *trie*, *Patricia tree*, *suffix automaton*.

*Note:
A variant, the compact DAWG, labels the edges with strings, not just single characters. In the compact DAWG, any **node* which is an only *child* is merged with its *parent* and the edge labels are concatenated. Another variant is the morphic DAWG, where some substrings are coded with new characters, like a simplified *Huffman coding*.

Author: PEB

## Implementation

JohnPaul Adamovsky's Directed Acyclic Word Graph or DAWG page with introduction, explanation, C implementation, and notes on optimization.
## More information

(1) **Andrew W. Appel and Guy J. Jacobson**, *The World's Fastest Scrabble Program*, CACM, 31(5):572-578, May 1988. Good description and comparison with a trie.

**M. Crochemore and R. Verin**, *Direct Construction of Compact Directed Acyclic Word Graphs*, 8th Annual Symposium, CPM 97, Aarhus, Denmark, 116-129, 1997.

(2) **J. Aoe, K. Morimoto, M. Shishibori and K-H. Park**, *A Trie Compaction Algorithm for a Large Set of Keys*, IEEE Trans. Knowledge and Data Engineering, 8(3):476-491, 1996.

**D. Perrin**, *Finite Automata*, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Elsevier, Amsterdam, Vol. A, 3-57, 1990.

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Entry modified 30 December 2011.

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Cite this as:

Paul E. Black, "directed acyclic word graph", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 30 December 2011. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/directedAcyclicWordGraph.html