Extracting Approximate Patterns

Pelfrêne, Johann; Alexandre, Joël

doi:10.1007/3-540-44888-8_24

Cited by 9 publications

(18 citation statements)

References 7 publications

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“…We briefly introduce basic definitions and results on maximal pattern enumeration according to [13,12]. For definitions not found here, see text books on string algorithms, e.g., [6,8].…”

Section: Maximal Motifsmentioning

confidence: 99%

“…In this subsection, we define merge and closure operations which are originally introduced in [2,3,12,13]. An infinite string is a function from integers to symbols in…”

Section: Merge and Closurementioning

confidence: 99%

“…The above definition is a generalization of the closure operation [11,16] from sets to motifs, and is introduced by [12,13].…”

Section: Property 4 Let X and Y Be Two Strings In σ(σ∪{•})mentioning

confidence: 99%

“…To overcome this problem, we focus on discovery of maximal motifs [9,12,13]. The semantics of a pattern x is given by the location list L(x) consisting of the positions in an input string s at which the pattern occurs.…”

Section: Introductionmentioning

confidence: 99%

“…Next, by examining the previous approaches [9,13,12], we present a simple output-polynomial time algorithm for maximal motif enumeration by breadth-first search, which possibly requires exponential space and delay. Then, we present an efficient algorithm that enumerates all maximal motifs in an input string of length n with O(n 3 ) time per motif with O(n) space and O(n 3 ) delay.…”

Section: Introductionmentioning

confidence: 99%

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An efficient polynomial space and polynomial delay algorithm for enumeration of maximal motifs in a sequence

Arimura

Uno

2006

J Comb Optim

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Abstract. In this paper, we consider the problem of enumerating all maximal motifs in an input string for the class of repeated motifs with wild cards. A maximal motif is such a representative motif that is not properly contained in any larger motifs with the same location lists. Although the enumeration problem for maximal motifs with wild cards has been studied in (Parida et al., CPM'01), (Pisanti et al.,MFCS'03) and (Pelfrene et al., CPM'03), its output-polynomial time computability has been still open. The main result of this paper is a polynomial space polynomial delay algorithm for the maximal motif enumeration problem for the repeated motifs with wild cards. This algorithm enumerates all maximal motifs in an input string of length n in O(n 3 ) time per motif with O(n) space, in particular O(n 3 ) delay. The key of the algorithm is depthfirst search on a tree-shaped search route over all maximal motifs based on a technique called prefix-preserving closure extension. We also show an exponential lower bound and a succinctness result on the number of maximal motifs, which indicate the limit of a straightforward approach. The results of the computational experiments show that our algorithm can be applicable to huge string data such as genome data in practice, and does not take large additional computational cost compared to usual frequent motif mining algorithms.

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“…We briefly introduce basic definitions and results on maximal pattern enumeration according to [13,12]. For definitions not found here, see text books on string algorithms, e.g., [6,8].…”

Section: Maximal Motifsmentioning

confidence: 99%

“…In this subsection, we define merge and closure operations which are originally introduced in [2,3,12,13]. An infinite string is a function from integers to symbols in…”

Section: Merge and Closurementioning

confidence: 99%

“…The above definition is a generalization of the closure operation [11,16] from sets to motifs, and is introduced by [12,13].…”

Section: Property 4 Let X and Y Be Two Strings In σ(σ∪{•})mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations