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## From Ukkonen to McCreight and Weiner: A Unifying View of Linear-Time Suffix Tree Construction (1997)

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### Other Repositories/Bibliography

Venue: | Algorithmica |

Citations: | 86 - 7 self |

### Citations

10603 | Introduction to Algorithms
- Cormen, Leiverson, et al.
- 2009
(Show Context)
Citation Context ...e and space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention sux trees, and never give ecient algorithms for their construction =-=[3, 20, 10, 1, 15, 6]-=-. Recent exceptions are [21, 12]. The reason for this is historical: starting with the seminal paper by Weiner [25], sux tree construction has built up a reputation of being overly complicated. The p... |

887 |
Data Structures and Algorithms.
- Aho, Ullman, et al.
- 1983
(Show Context)
Citation Context ...d space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention suffix trees, and never give efficient algorithms for their construction =-=[3, 21, 11, 1, 17, 7]-=-. Recent exceptions are [22, 13]. The reason for this is historical: starting with the seminal paper by Weiner [26], suffix tree construction has built up a reputation of being overly complicated. The... |

785 |
Efficient string matching: an aid to bibliographic search.
- Aho, Corasick
- 1975
(Show Context)
Citation Context ... atomic, if every edge in T is marked by a single character. T is compact, if every node in T is either the root, a leaf, or a branching node. 2 Atomic A + -trees are also known under the name "t=-=rie" [2]-=-. Both atomic and compact A + - trees are uniquely determined by the words occurring in them. In an atomic A + -tree every node is explicit. In a compact A + -tree, nodes with a single outgoing edge a... |

516 |
Algorithms in C++.
- Sedgewick
- 1995
(Show Context)
Citation Context ...e and space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention sux trees, and never give ecient algorithms for their construction =-=[3, 20, 10, 1, 15, 6]-=-. Recent exceptions are [21, 12]. The reason for this is historical: starting with the seminal paper by Weiner [25], sux tree construction has built up a reputation of being overly complicated. The p... |

375 |
Text Algorithms.
- Crochemore, Rytter
- 1994
(Show Context)
Citation Context ... string processing, elementary books on algorithms and data structures barely mention sux trees, and never give ecient algorithms for their construction [3, 20, 10, 1, 15, 6]. Recent exceptions are =-=[21, 12]-=-. The reason for this is historical: starting with the seminal paper by Weiner [25], sux tree construction has built up a reputation of being overly complicated. The purpose of the present paper is t... |

215 |
Approximate string matching with q-grams and maximal matches
- Ukkonen
- 1992
(Show Context)
Citation Context ...nicely summarizes the additional power of sux links that makes them useful in many contexts. For example, such an automaton can be used to compute the matching statistics in [8], the q-gram distance =-=[23]-=-, or the shift-table for the Boyer-Moore algorithm [16]. 2.6 Dualities between Sux Trees and Sux Links We now study the deeper relation between sux trees and their sux links. First we note that th... |

150 |
Algorithms for finding patterns in strings. In
- Aho
- 1990
(Show Context)
Citation Context ...d space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention suffix trees, and never give efficient algorithms for their construction =-=[3, 21, 11, 1, 17, 7]-=-. Recent exceptions are [22, 13]. The reason for this is historical: starting with the seminal paper by Weiner [26], suffix tree construction has built up a reputation of being overly complicated. The... |

129 |
The myriad virtues of subword trees.
- Apostolico
- 1985
(Show Context)
Citation Context ... Key Words. Text processing. Online string matching. Suffix trees. Linear time algorithm. Program transformation. 1 Motivation and Overview Suffix trees provide most efficient solutions to a "myr=-=iad" [4]-=- of string processing problems. The suffix tree for a string t really turns t inside out, immediately exposing properties like longest or most frequent subwords. The fundamental question whether w occ... |

117 |
String searching algorithms
- Stephen
- 1994
(Show Context)
Citation Context ... string processing, elementary books on algorithms and data structures barely mention sux trees, and never give ecient algorithms for their construction [3, 20, 10, 1, 15, 6]. Recent exceptions are =-=[21, 12]-=-. The reason for this is historical: starting with the seminal paper by Weiner [25], sux tree construction has built up a reputation of being overly complicated. The purpose of the present paper is t... |

111 |
The smallest automaton recognizing the subwords of a text.
- Blumer, Blumer, et al.
- 1985
(Show Context)
Citation Context ...mma \Gamma \Gamma\Psi ceae a e a 1. ast(t) has O(n 2 ) nodes (take e.g. t = a n c n in Figure 4). However, isomorphic subtrees 2 can be shared [10]. Sharing brings the space requirements down to O(n) =-=[8, 12]-=-. However, subtree sharing may be impossible, when leaves are to be annotated with extra information. 2. cst(t) has O(n) nodes, as all inner nodes are branching, and there are at most n leaves. The ed... |

95 |
pattern matching algorithms
- Linear
- 1973
(Show Context)
Citation Context ...ux trees, and never give ecient algorithms for their construction [3, 20, 10, 1, 15, 6]. Recent exceptions are [21, 12]. The reason for this is historical: starting with the seminal paper by Weiner =-=[25]-=-, sux tree construction has built up a reputation of being overly complicated. The purpose of the present paper is to correct this reputation | by working out what is essential about ecient sux tre... |

65 |
A space-economical sux tree construction algorithm
- McCreight
- 1976
(Show Context)
Citation Context ...om the International Computer Science Institute, Berkeley, CA; This article appeared in Algorithmica, 19:331-353, 1997 1 More precisely, we review the linear time algorithms of Weiner [25], McCreight =-=[17]-=-, and Ukkonen [24]. Let us call these algorithms wrf,1 mcc, and ukk. We use the terminology of the most recent algorithm, Ukkonen's online construction, to explain its predecessors. This reveals relat... |

51 |
Approximate string matching in sublinear expected time
- Chang, Lawler
- 1990
(Show Context)
Citation Context ...is taken from [20]. It nicely summarizes the additional power of suffix links that makes them useful in many contexts. For example, such an automaton can be used to compute the matching statistics in =-=[9]-=-, the q-gram distance [24], or the shift-table for the Boyer-Moore algorithm [18]. 2.6 Dualities between Suffix Trees and Suffix Links We now study the deeper relation between suffix trees and their s... |

40 |
Ecient string matching: an aid to bibliographic search
- Aho, Corasick
- 1975
(Show Context)
Citation Context ...is atomic, if every edge in T is marked by a single character. T is compact, if every node in T is either the root, a leaf, or a branching node. 2 Atomic A+-trees are also known under the name \trie" =-=[2]-=-. Both atomic and compact A+- trees are uniquely determined by the words occurring in them. In an atomic A+-tree every node is explicit. In a compact A+-tree, nodes with a single outgoing edge are imp... |

32 |
Efficient and elegant subword tree construction.
- Chen, Seiferas
- 1985
(Show Context)
Citation Context ...a\Psi ceae a e a ceaceae a a ? c a ? e a ? a a @ @ @R \Gamma \Gamma \Gamma\Psi ceae a e a 1. ast(t) has O(n 2 ) nodes (take e.g. t = a n c n in Figure 4). However, isomorphic subtrees 2 can be shared =-=[10]-=-. Sharing brings the space requirements down to O(n) [8, 12]. However, subtree sharing may be impossible, when leaves are to be annotated with extra information. 2. cst(t) has O(n) nodes, as all inner... |

26 | Self-alignments in words and their applications
- Apostolico, Szpankowski
- 1992
(Show Context)
Citation Context ... if necessary, and adds an edge u v - uv. Later authors will suggest similar naive versions of other algorithms [19, 15], and it will be shown that their efficiency is O(n log n) in the expected case =-=[6]-=-. The factor log n comes from walking the tree from the root to the point of insertion. For an O(n)-algorithm we must access this point in O(1). As the string u above equals ff \Gamma1 (as), our probl... |

18 |
Introduction to algorithms, The MIT press,
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...d space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention suffix trees, and never give efficient algorithms for their construction =-=[3, 21, 11, 1, 17, 7]-=-. Recent exceptions are [22, 13]. The reason for this is historical: starting with the seminal paper by Weiner [26], suffix tree construction has built up a reputation of being overly complicated. The... |

14 | Combinatorial Algorithms on Words - Apostolico, Galil - 1985 |

14 |
String matching with constraints
- Crochemore
- 1988
(Show Context)
Citation Context ...mma \Gamma \Gamma\Psi ceae a e a 1. ast(t) has O(n 2 ) nodes (take e.g. t = a n c n in Figure 4). However, isomorphic subtrees 2 can be shared [10]. Sharing brings the space requirements down to O(n) =-=[8, 12]-=-. However, subtree sharing may be impossible, when leaves are to be annotated with extra information. 2. cst(t) has O(n) nodes, as all inner nodes are branching, and there are at most n leaves. The ed... |

13 |
Fundamental Algorithms for a Declarative Pattern Matching System. Dissertation, Technische Fakultat, Universitat Bielefeld, available as Report 95-03
- Kurtz
- 1995
(Show Context)
Citation Context ...at makes them useful in many contexts. For example, such an automaton can be used to compute the matching statistics in [8], the q-gram distance [23], or the shift-table for the Boyer-Moore algorithm =-=[16]-=-. 2.6 Dualities between Sux Trees and Sux Links We now study the deeper relation between sux trees and their sux links. First we note that the sux links form a tree themselves. Denition 9 The su... |

9 |
On-line Construction of Sux-Trees
- Ukkonen
- 1995
(Show Context)
Citation Context ...al Computer Science Institute, Berkeley, CA; This article appeared in Algorithmica, 19:331-353, 1997 1 More precisely, we review the linear time algorithms of Weiner [25], McCreight [17], and Ukkonen =-=[24]-=-. Let us call these algorithms wrf,1 mcc, and ukk. We use the terminology of the most recent algorithm, Ukkonen's online construction, to explain its predecessors. This reveals relationships much clos... |

6 |
Text Algorithms
- Gonnet, Baeza-Yates
- 1991
(Show Context)
Citation Context ...e and space. In spite of their basic role for string processing, elementary books on algorithms and data structures barely mention sux trees, and never give ecient algorithms for their construction =-=[3, 20, 10, 1, 15, 6]-=-. Recent exceptions are [21, 12]. The reason for this is historical: starting with the seminal paper by Weiner [25], sux tree construction has built up a reputation of being overly complicated. The p... |

5 |
Sux Trees in the Functional Programming Paradigm
- Giegerich, Kurtz
- 1994
(Show Context)
Citation Context ...y the leaf edge y xv- uv. 2. If u is not a leaf in cst(s) then the algorithm splits for u if necessary, and adds an edge u v- uv. Later authors will suggest similar naive versions of other algorithms =-=[17, 13]-=-, and it will be shown that their eciency is O(n log n) in the expected case [5]. The factor log n comes from walking the tree from the root to the point of insertion. For an O(n)-algorithm we must a... |

4 |
String Searching Algorithms
- Baeza-Yates
- 1992
(Show Context)
Citation Context |

3 |
A Comparison of Imperative and Purely Functional Sux Tree Constructions
- Giegerich, Kurtz
(Show Context)
Citation Context ...sible input. 3. This transformation sacrices the online property. mcc will always read ahead of ukk in t. This lookahead is quantied in Proposition 5. Assertion 2 is conrmed by the measurements in =-=[14]-=-. In fact, this invariance of the relative eciency of ukk and mcc made ussrst wonder about a deeper relationship between these two algorithms. We were incited further by a note in [24], where Ukkonen... |

3 |
Symmetry Breaking for Sux Tree Construction
- ahinalp, Vishkin
- 1994
(Show Context)
Citation Context ...al way to express this, we conjecture that any sequential sux tree construction not based on these concepts will fail to meet the O(n)-criterion. This does not pertain to parallel constructions like =-=[19]-=-. 22 8 Acknowledgments Gene Lawler encouraged us to exploit our duality observation for explaining sux tree construction. Dan Guseld and Richard Karp directed our attention to the manuscript by Prat... |