Average-optimal single and multiple approximate string matching

Fredriksson, Kimmo; Navarro, Gonzalo

doi:10.1145/1005813.1041513

Cited by 41 publications

(50 citation statements)

References 28 publications

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“…Still another type is relaxed preprocessing with a reduced alphabet [29,30]. In approximate string matching this extends the applicability of the Four-Russians technique [31,32], which is used to precompute edit distances between arbitrary q-grams and the q-grams of a pattern.…”

Section: Alphabet Transformations In String Matchingmentioning

confidence: 99%

Approximate String Matching with Reduced Alphabet

Salmela

Tarhio

2010

Algorithms and Applications

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Abstract. We present a method to speed up approximate string matching by mapping the factual alphabet to a smaller alphabet. We apply the alphabet reduction scheme to a tuned version of the approximate BoyerMoore algorithm utilizing the Four-Russians technique. Our experiments show that the alphabet reduction makes the algorithm faster. Especially in the k-mismatch case, the new variation is faster than earlier algorithms for English data with small values of k.

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Section: Alphabet Transformations In String Matchingmentioning

confidence: 99%

Approximate String Matching with Reduced Alphabet

Salmela

Tarhio

2010

Algorithms and Applications

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“…Average-optimal filtering method [Fredriksson and Navarro 2004], using hierarchical verification with BPM in verifying full matches. Implemented by its original authors.…”

Section: Approximate String Matching: a Single Patternmentioning

confidence: 99%

“…The algorithms included in these experiments were the most promising ones according to the most recent work [Fredriksson and Navarro 2004]…”

Section: Approximate String Matching: Several Patternsmentioning

confidence: 99%

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Increased bit-parallelism for approximate and multiple string matching

Hyyrö

Fredriksson

Navarro

2005

ACM J. Exp. Algorithmics

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Bit-parallelism permits executing several operations simultaneously over a set of bits or numbers stored in a single computer word. This technique permits searching for the approximate occurrences of a pattern of length m in a text of length n in time O(⌈m/w⌉n), where w is the number of bits in the computer word. Although this is asymptotically the optimal bit-parallel speedup over the basic O(mn) time algorithm, it wastes bit-parallelism's power in the common case where m is much smaller than w, since w − m bits in the computer words get unused.In this paper we explore different ways to increase the bit-parallelism when the search pattern is short. First, we show how multiple patterns can be packed into a single computer word so as to search for all them simultaneously. Instead of spending O(rn) time to search for r patterns of length m ≤ w/2, we need O(⌈rm/w⌉n) time. Second, we show how the mechanism permits boosting the search for a single pattern of length m ≤ w/2, which can be searched for in O(⌈n/⌊w/m⌋⌉) bit-parallel steps instead of O(n). Third, we show how to extend these algorithms so that the time bounds essentially depend on k instead of m, where k is the maximum number of differences permitted. Finally, we show how the ideas can be applied to other problems such as multiple exact string matching and one-against-all computation of edit distance and longest common subsequences.Our experimental results show that the new algorithms work well in practice, obtaining significant speedups over the best existing alternatives especially on short patterns and moderate number of differences allowed. This work fills an important gap in the field, where little work has focused on very short patterns.

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“…Let us first review the non-transposition invariant algorithms. In [12] it is shown how to perform approximate searching (under edit distance) of r patterns of length u in a text of length n, with distance at most k, in optimal average time…”

Section: Featuresmentioning

confidence: 99%

Rotation and Lighting Invariant Template Matching

Fredriksson

Mäkinen

Navarro

2004

LATIN 2004: Theoretical Informatics

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We address the problem of searching for a two-dimensional pattern in a two-dimensional text (or image), such that the pattern can be found even if it appears rotated and it is brighter or darker than its occurrence. Furthermore, we consider approximate matching under several tolerance models. We obtain algorithms that are almost optimal both in the worst and the average cases simultaneously. The complexities we obtain are very close to the best current results for the case where only rotations, but not lighting invariance, are supported. These are the first results for this problem under a combinatorial approach.

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Average-optimal single and multiple approximate string matching

Cited by 41 publications

References 28 publications

Approximate String Matching with Reduced Alphabet

Approximate String Matching with Reduced Alphabet

Increased bit-parallelism for approximate and multiple string matching

Rotation and Lighting Invariant Template Matching

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