Speeding up the cyclic edit distance using LAESA with early abandon

Abstract

The cyclic edit distance between two strings is the minimum edit distance between one of this strings and every possible cyclic shift of the other. This can be useful, for example, in image analysis where strings describe the contour of shapes or in computational biology for classifying circular permuted proteins or circular DNA/RNA molecules.The cyclic edit distance can be computed in O(mn log m) time, however, in real recognition tasks this is a high computational cost because of the size of databases. A method to reduce the number of comparisons and avoid an exhaustive search is convenient. In this work, we present a new algorithm based on a modification of LAESA (Linear Approximating and Eliminating Search Algorithm) for applying pruning in the computation of distances. It is an efficient procedure for classification and retrieval of cyclic strings. Experimental results show that our proposal considerably outperforms LAESA.

Circular Pattern Matching with k Mismatches

“…In many real-world applications, such as in bioinformatics [4,22,25,7] or in image processing [3,33,34,32], any cyclic shift (rotation) of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P , if this distance is no more than k. This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers [17,8,6,5,9,24] have thus been devoted to solving the k-CPM problem but, to the best of our knowledge, only average-case upper bounds are known; i.e.…”

“…The CPM problem can also be solved in O(n) time [15]. Applications where circular strings are considered include the comparison of DNA sequences in bioinformatics [24,4] as well as the comparison of shapes represented through directional chain codes in image processing [37,36]. In both applications, it is not sufficient to look for exact (circular) matches.…”

Bounding Edit Distance for similarity-based sequence classification on Structural Pattern Recognition

“…As of the NN algorithm bottleneck, the main issue of this classifier is that no To our best knowledge, the only formal study with a similar idea focusing on string data is found in the work by Palazón-González and Marzal [20], in which 115 the Linear Approximating and Eliminating Search Algorithm (LAESA) [21] Fast Similarity Search method is combined with some distance bounds for the case of the cyclic edit distance. In our work, we further explore this idea of distance bounds generalizing the data representation considered to sequences of vectors, instead of exclusively examining string data, and thus obtaining remarkable 120 reductions in terms of time consumption.…”