Giegerich, R. and Kurtz, S. (1995) A comparison of imperative and purely functional sux tree constructions. Science of Computer Programming 25, 187-218.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....algorithm is based on a data structure called suffix trie. It is a simplified but more resource demanding version of the well known suffix tree (McCreight 1976; Ukkonen 1995) We construct a suffix trie for our set of sequences G. Our construction procedure is inspired by the lazy algorithm of (Giegerich and Kurtz 1995) for generating suffix trees. The resulting trie represents all the patterns (in the chosen class of patterns) that are present in some sequence in G. The nodes of the trie are labeled with symbols from the pattern representation alphabet: the individual nucleotides, wild cards, or character ....

Giegerich, R. and S. Kurtz. 1995. A comparison of imperative and purely functional suffix tree constructions.

....Section 5.2) we had a set of 6000 sequences of lengths between 100 and 1200. The number of occurrences for the most interesting patterns were not known a priori. We developed a pattern discovery algorithm based on the suffix tree data structure [21, 35] The lazy suffix tree generation algorithm [12] was extended for generating the suffixes of all sequences in the set, and further, to generate only the patterns that match the sufficient number of examples. The generated patterns are maintained in a trie structure that is expanded in a systematic way. The patterns are generated simultaneously ....

R. Giegerich and S. Kurtz. A comparison of imperative and purely functional suffix tree constructions. Science of Computer Programming, 25(2--3):187--218, 1995.

....a simplified but more resources demanding version of the well known data structure suffix tree [Wei73, McC76, Ukk95] for a textbook presentation, see for example [Gus97] We construct the suffix trie for the set of input strings S. Our construction procedure is inspired by the lazy algorithm of [GK95] for generating suffix trees. The resulting trie represents all the patterns (in the chosen class of patterns) that are present in some string in S. The nodes of the trie are labeled with symbols from the pattern representation alphabet: the individual characters, wildcards, or character groups ....

....the space required for storing the full suffix tree can be too large. In an efficient implementation the size of the tree is in average about 10 15 times the size of S. Also, due to non locality properties of linear time suffix tree generation algorithms, it is hard to avoid memory paging problems [GK95]. We are interested only in the patterns that occur at least K times in S. It seems that unnecessary work has been done by constructing the subtrees with less than K leaves. Thus, there might be better algorithms that do not build the full suffix tree but only the part that contains the most ....

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R. Giegerich and S. Kurtz. A comparison of imperative and purely functional suffix tree constructions. Science of Computer Programming, 25(2--3):187--218, 1995.

.... following reasons: At first, we do not need the additional virtue of Ukkonen s algorithm (it is online) and of Farach s algorithm (it can handle integer alphabets) Second, McCreight s algorithm is more space efficient than Weiner s algorithm, and slightly faster than Ukkonen s method, as shown in [9]. We have not seen any practical results of the space and time behavior of Farach s algorithms. We note that McCreight s algorithm also requires the sentinel character appended to the input sequence x. Thus it is well suited for computing the Burrows and Wheeler Transformation. 3.3 Decoding ....

R. Giegerich and S. Kurtz. A Comparison of Imperative and Purely Functional Suffix Tree Constructions. Science of Computer Programming, 25(2- 3):187--218, 1995.

....shown that Ukkonen s suffix tree algorithm constructs the nodes and edges of the suffix tree in the same order as McCreight s algorithm. As a consequence, one could instead use Ukkonen s algorithm. We prefer McCreight s algorithm, since it is slightly faster than Ukkonen s algorithm, as shown in [GK95] It is easy to see that the functions insertleaf and insertbranch can be implemented in constant time. Thus it remains to show how to ffl decide whether a branching node is small or large, ffl set the distance of a small node, ffl determine headloc i and tailptr i in constant amortized time. ....

....the list of successors of a particular node. Each such traversal step requires only a few very simple and fast operations. But the nodes accessed during such a traversal may be stored at very distant locations in memory, which means that McCreight s algorithm has a poor locality behavior (see [GK95] If the text is short, then the entire suffix tree representation usually fits into the cache, so that cache misses are rare. So the poor locality does not matter, and hence the good performance of the linked list implementations for the case that the alphabet and the text are small. For larger ....

R. Giegerich and S. Kurtz. A Comparison of Imperative and Purely Functional Suffix Tree Constructions. Science of Computer Programming, 25(2-3):187--218, 1995.

....related data structures, it will give mcc a minor efficiency advantage over ukk, on every possible input. 3. This transformation sacrifices the online property. mcc will always read ahead of ukk in t. This lookahead is quantified in Proposition 5.5. Assertion 2 is confirmed by the measurements in [16]. In fact, this invariance of the relative efficiency of ukk and mcc made us first wonder about a deeper relationship between these two algorithms. We were incited further by a note in [25] where Ukkonen remarks that on the technical level, the main difference between ukk and mcc lies in the way ....

....confirms, concretizes, and explains this observation. 4 Development of ukk and mcc 4.1 A Short Derivation of ukk Space does not allow a complete derivation of ukk here. We only give a short explanation together with the concrete algorithm, and refer the reader to the development in [25] or [16]. Online construction means generating a series of suffix trees for longer and longer prefixes of t. While cst( is trivial (just the root with no edges) we study the step from cst(p) to cst(pa) where p is a prefix of t, and a is the next character in t to be read. To construct cst(pa) we ....

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R. Giegerich and S. Kurtz. A Comparison of Imperative and Purely Functional Suffix Tree Constructions. Science of Computer Programming, 25(2-3):187--218, 1995.

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Giegerich, R. and Kurtz, S. (1995) A comparison of imperative and purely functional sux tree constructions. Science of Computer Programming 25, 187-218.

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R. Giegerich and S. Kurtz. A Comparison of Imperative and Purely Functional Suffix Tree Constructions. Science of Computer Programming, 25(2-3):187--218, 1995.

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