E. Ukkonen. Constructing suffix-trees on-line in linear time. Algorithms, 1(92):484--492, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a given string. The overall space requirement of the suffix tree is linear in the length of the string it represents. Various approaches of building the substring index in linear time have been developed. McCreight s algorithm builds a suffix tree in linear time and is space efficient[i] Ukkonen [2] developed a linear time, on line suffix tree construction algorithm. Searching for all instances of a substring S in a suffix tree is easy since the symbols in S define a path down the suffix tree. Following this path, if we encounter a before reaching the end, then S is not in the tree. If we ....

Ukkonen, E. (1992) "Constructing suffix-trees on-line in linear time," in Leeuwen, J. van(ed.) In Algorithms, Software, Architecture: Information Processing 92, Vol. 1, pp. 484-92, Elsevier, Amsterdam.

....Tables to Weighted Sequences During the index construction, a trie is employed as an intermediary structure to facilitate the building of the isodepth index. The trie is not used during query processing. Various approaches to build tries or suffix trees in linear time have been developed. Ukkonen [19], for instance, developed a linear time, on line suffix tree construction algorithm. We do not address the details of building suffix trees in this paper. The suffix tree, however, only supports efficient matching of contiguous substrings. If a query string contains gaps, for instance, ....

....are generated. 2. Since # is an ancestor of , we have # # # and # # # # # . From , we get # # , which means # is an ancestor of # . Algorithm 1 summarizes the index construction procedure. The construction is of time complexity ### # . The well known Ukkonen algorithm [19] builds suffix tree in linear time. The construction of the trie used for iso depth indexing is less time consuming because the length of the subsequences inserted into the trie is constrained by # , the window size. Thus, a brute force algorithm [14] can construct the trie in linear time. For ....

E. Ukkonen. Constructing suffix-trees on-line in linear time. Algorithms, Software, Architecture: Information Processing, pages 484--92, 1992.

....more than once. Every substring of T can be found by traversing a path from the root, possibly continuing the search directly in the text if a leaf is reached. In practice a suffix tree, obtained by compressing unary trie paths, is preferred because it yields O(n) space and O(n) construction time [12, 24] and offers the same functionality. Figure 1 illustrates a suffix trie. 6 4 c 10 3 11 7 10 8 1 4 6 2 9 5 3 Text r a r d 7 c 5 2 9 c a a r 8 1 c 11 b d c a Suffix Trie Suffix Array Figure 1: The suffix trie and suffix ....

....u r g e r y 0 1 2 3 4 5 6 7 s 1 0 1 2 3 4 5 6 u 2 1 0 1 2 3 4 5 r 3 2 1 0 1 2 3 4 v 4 3 2 1 1 2 3 4 e 5 4 3 2 2 1 2 3 y 6 5 4 3 3 2 2 2 Figure 2: The dynamic programming algorithm run over the suffix trie. We show only one path and one additional link. Some improvements to this algorithm [10, 24, 5] avoid processing some redundant nodes at the cost of a more complex node processing, but their practicality has not been established. This method has been used also to compare a whole text against other or against itself [3] 4 Partitioning into Exact Search Each approximate occurrence of a ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, 1995.

....path store the whole string that they represent (via two pointers to their initial and final text position) Once unary paths are not present the trie, now called suffix tree, has O(n) nodes instead of the worst case O(n ) of the trie. The suffix tree can be directly built in O(n) time [22, 35]. Any algorithm on a suffix trie can be simulated at the same cost in the suffix tree. We call explicit those suffix trie nodes that survive in the suffix tree, and implicit those that are collapsed. Figure 1 shows the suffix trie and tree of the text abracadabra . Note that a special endmarker ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, 1995.

....path store the whole string that they represent (via two pointers to their initial and final text position) Once unary paths are not present the trie, now called suffix tree, has O(n) nodes instead of the worst case O(n 2 ) of the trie. The suffix tree can be directly built in O(n) time [25, 38]. Any algorithm on a suffix trie can be simulated at the same cost in the suffix tree. We call explicit those suffix trie nodes that survive in the suffix tree, and implicit those that are collapsed. Figure 1 shows the suffix trie and tree of the text abracadabra . Note that a special endmarker ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, 1995.

....of word is difficult to define (as in oriental languages) or in agglutinating languages such as Finnish. Our focus in this paper is sequence retrieving indexes. Among these, we find two types of approaches. A first type is based on simulating a sequential algorithm, running it on the suffix tree [21, 1, 38] or DAWG (directed acyclic word graph) 12, 9] of the text instead of the text itself. A suffix trie is a trie where all the suffixes of the text string have been inserted. A suffix tree achieves O(n) worst case space and construction time by compressing unary paths of the suffix trie. A DAWG is ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, Sep 1995.

....exactly in the sequence(s) We start by looking on this new way of solving the problem when repeated motifs are sought. 3 Solving the Repeated Motifs Problem 3.1 Preprocessing Constructing the Suffix Tree. We do not describe the suffix tree construction, this can be found in either [12] [19] or (for a review of this and other data structures and text algorithms) 6] and [8] We just recall here some of the basic properties of such structures (these are taken from [12] Basic Properties of the Suffix Tree T of a Sequence s. 1. A branch of T may represent any nonempty substring of ....

....an occurrence implies more work. This however increases the algorithm s time and space complexity by a constant factor only. 3. 3 Complexity Assuming an alphabet of fixed size, a compact suffix tree T may be constructed in O(n) time where n is the length of sequence s and occupies O(n) space [12] [19]. Adding information to the nodes of the tree as described in section 3.1 takes time O(n) and requires O(1) space per node of T . Concerning the spelling operation, we have that: Lemma 2. Spelling all valid models for the Repeated Motifs Problem given T requires O(nV(e; k) time where k is ....

E. Ukkonen. Constructing suffix trees on-line in linear time. pages 484--492. IFIP'92, 1992.

....strings. Thus our special case involves only tail insertions. We propose a series of data structures based on suffix trees [14] to efficiently support a restricted set of these operations. In particular, we build our data structure around Ukkonen s linear time suffix tree construction algorithm [24]. In Ukkonen s algorithm, suffixes are inserted into the tree from left to right. Analogously, we can continue to append new characters onto the end of a string by simulating the insertion of another subsequent suffix. We will augment this suffix tree to support constant time least common ancestor ....

E. Ukkonen. Constructing suffix trees on-line in linear time. In Intern. Federation of Information Processing (IFIP '92), pages 484--492, 1992.

....to index a fixed set of words in a text database. For general purpose strings for which the data processing unit is substrings, there is no clear cut of words . Taking all possible substrings as words leads to the blowup of O(n 2 ) words for a string of length n. The suffix tree indexing [C95, M76, LV89, U92, U93, W73] was previously used to speed up subsequent search of substrings. The update of the suffix tree was considered in [M76] for dynamic strings, by assuming that a position number never changes once assigned. Such position numbers do not correspond to the logical ordering of characters and are ....

....tree serves a natural and compact representation of sequential patterns. In this paper, we adopt the suffix tree for indexing substrings, with the focus on updating the suffix tree for solving the incremental discovery problem. The following briefly introduces the suffix tree. The suffix tree [LV89, M76, S94, U92]. Assume that no suffix of S is a prefix of a different suffix of S. This can be satisfied by appending the unique delimiter at the right extreme of S. S can be mapped to a tree T in which root to leaf paths are suffixes of S and terminal nodes represent uniquely starting positions of suffixes. ....

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E. Ukkonen, "Constructing suffix-trees on-line in linear time", Algorithms, Software, Architecture: Information Processing 92, Vol. 1, 484-492, Elsevier, Amsterdam

....of a pattern of length m in O(m) time. To reduce the high space requirements, a Patricia tree can be used [14] which compresses unary paths to achieve O(n) storage cost. A Patricia tree built over all suffixes of the text is called a suffix tree [12] Suffix trees take time O(n) to build [20]. However, this construction is only practical if the tree fits in main memory. Suffix arrays further reduce the space requirements by storing only the leaves of suffix trees. Recently, an intermediate structure between suffix trees and suffix arrays has been proposed [9] 1.2 Distributed Parallel ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, Sep 1995.

....substrings that can be prefixes of an approximate occurrence of the pattern. The algorithms traverse in the suffix tree all the different viable prefixes, simulating the dynamic programming algorithm. A suffix tree can be built in linear time with respect to the text size, given enough main memory [26, 39]. In the improved version [11] the complexity of the search is O(mQ) plus the size of the output, where Q is the number of distinct viable prefixes in the text (Q n) In [38] a worst case analysis shows that Q = O(min(n; m k 1 oe k ) where oe is the alphabet size. If k is small, Q n. ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, Sep 1995.

....from the current one) The occurrences are found in ascending order, hence each insertion takes O(1) time. Therefore, this index is built in O(n) expected time and a single pass over the text. The worst case can be made O(n) by modifying Ukkonen s technique to build a suffix tree in linear time [26]. We analyze space now. To determine the number of different q grams in random text, consider that there are oe q different urns (q grams) and n balls (q grams in the text) The probability of a q gram to be selected in a trial is 1=oe q . Therefore, the probability of a q gram not being ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, Sep 1995.

....one of the most important data structures in stringology. The suffix tree is an index like structure formed from a string that allows many kinds of fast queries about the string. What makes the suffix tree attractive is that its size and its construction time are linear in the length of the text [19, 14, 17]. Suffix trees have a wide variety of applications. Apostolico [4] cites over forty references on suffix trees, and Manber and Myers [13] mention several newer ones. The application, that we are mostly interested in in this paper, is the use of a suffix tree as an index of a large static text to ....

....aa b a c c a c a 0 1 2 3 4 5 6 7 0 1 7 2 4 3 6 1 5 a a b a c c a a c c a b a c c a c a c a b a c c a c c a Fig. 2. a) Suffix tree and b) suffix array for string cabacca . If the alphabet size j Sigma j is considered constant, the suffix tree can be constructed in time O(n) [19, 14, 17] and string matching takes time O(m) The dependency on j Sigma j may be linear, logarithmic or constant depending on the implementation of branching. The most compact alternative uses linked lists and has linear dependency on j Sigma j. In regular expression matching and approximate string ....

[Article contains additional citation context not shown here]

E. Ukkonen. Constructing suffix trees on-line in linear time. In J. van Leeuwen, editor, Algorithms, Software, Architecture. Information Processing 92, volume 1, pages 484--492, 1992. Full version is to appear in Algorithmica.

....from the current one) The occurrences are found in ascending order, hence each insertion takes O(1) time. Therefore, this index is built in O(n) expected time and a single pass over the text. The worst case can be made O(n) by modifying Ukkonen s technique to build a suffix tree in linear time [31]. 4.2 Index Space We analyze space now. To determine the number of different q grams in random text, consider that there are oe q different urns (q grams) and n balls (q grams in the text) The probability of a q gram to be selected in a trial is 1=oe q . Therefore, the probability of a ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249--260, Sep 1995.

....unary paths. At the nodes which root a compressed path, an indication of how many characters to skip is stored. Once unary paths are not present the tree has O(n) nodes instead of the worst case O(n 2 ) of the trie (see Figure 2. 7) This structure can be built in time O(n) where n = jSj [McC76, Ukk95] It is a very useful structure to solve many problems [AG85, Apo85] r b a a c a d a b r a 1 2 3 4 6 5 7 8 9 10 11 6 4 b r a r a c d 7 c 5 2 9 c a a r 8 1 c 11 b d 10 3 c 6 4 3 10 8 1 b r d 7 c 5 a 11 b d c 1 3 c 4 2 ....

....from the current one) The occurrences are found in ascending order, hence each insertion takes O(1) time. Therefore, this index is built in O(n) expected time and a single pass over the text. The worst case can be made O(n) by modifying Ukkonen s technique to build a suffix tree in linear time [Ukk95] we only want the tree up to height q) 9.1.2.2 Index Space We analyze space now. To determine the number of different q grams in random text, consider that there are oe q different urns (q grams) and n balls (q grams in the text) to be assigned to the urns. The probability of a q gram ....

E. Ukkonen. Constructing suffix trees on-line in linear time. Algorithmica, 14(3):249-- 260, Sep 1995.

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E. Ukkonen, Constructing suffix trees on--line in linear time, in Algorithms, Software, Architecture. Information Processing 92, vol. I (J. van Leeuwen, ed.), Elsevier, 1992, pp. 484--492.

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E. Ukkonen. Constructing suffix-trees on-line in linear time. Algorithms, 1(92):484--492, 1992.

No context found.

E. Ukkonen. Constructing Suffix-trees On-Line in Linear Time. Algorithms, Software, Architecture: Information Processing, 1(92):484--92, 1992.

No context found.

E. Ukkonen. Constructing Suffix-trees On-Line in Linear Time. Algorithms, Software, Architecture: Information Processing, 1(92):484--92, 1992.

No context found.

E. Ukkonen. Constructing Suffix Trees On-line in Linear Time. In Proceedings of the 12th IFIP World Computer Congress, pages 484--492, 1992.

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E. Ukkonen. Constructing suffix-trees on-line in linear time. Algorithms, Software, Architecture: Information Processing, pages 484--92, 1992.

No context found.

E. Ukkonen. Constructing Suffix Trees On-line in Linear Time. In Proceedings of the 12th IFIP World Computer Congress, pages 484--492, 1992.

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E. Ukkonen, "Constructing Suffix Trees On-Line in Linear Time", Proc. IFIP 12th World Computer Congress, 1992.

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E. Ukkonen. Constructing Suffix Trees On-line in Linear Time. In Algorithms, Software, Architecture. J.v.Leeuwen (Ed.), Information Processing 92, Volume I, pages 484--492. Elsevier, 1992.

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E. Ukkonen. Constructing Suffix Trees On-line in Linear Time. Algorithms, Software, Architecture. J.v.Leeuwen (Ed.), Inform. Processing 92, Vol. I, pages 484--492, 1992.

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