Behshad Behzadi

DNA compression challenge revisited: a dynamic programming approach

Standard compression algorithms are not able to compress DNA sequences. Recently, new algorithms have been introduced specifically for this purpose, often using detection of long approximate repeats. In this paper, we present another algorithm, DNAPack, based on dynamic programming. In comparison with former existing programs, it compresses DNA slightly better, while the cost of dynamic programming is almost negligible.

Alignment of minisatellite maps based on run-length encoding scheme.

Subsequent duplication events are responsible for the evolution of the minisatellite maps. Alignment of two minisatellite maps should therefore take these duplication events into account, in addition to the well-known edit operations. All algorithms for computing an optimal alignment of two maps, including the one presented here, first deduce the costs of optimal duplication scenarios for all substrings of the given maps. Then, they incorporate the pre-computed costs in the alignment recurrence. However, all previous algorithms addressing this problem are dependent on the number of distinct map units (map alphabet) and do not fully make use of the repetitiveness of the map units. In this paper, we present an algorithm that remedies these shortcomings: our algorithm is alphabet-independent and is based on the run-length encoding scheme. It is the fastest in theory, and in practice as well, as shown by experimental results. Furthermore, our alignment model is more general than that of the previous algorithms, and captures better the duplication mechanism. Using our algorithm, we derive a quantitative evidence that there is a directional bias in the growth of minisatellites of the MSY1 dataset.

The Minisatellite Transformation Problem Revisited: A Run Length Encoded Approach

In this paper we present a more efficient algorithm for comparison of minisatellites which has complexity O(n’3+ m’3 + mn’2+ nm’2 +mn) where n and m are the lengths of the maps and n’ and m’ are the sizes of run-length encoded maps. We show that this algorithm makes a significant improvement for the real biological data, dividing the computing time by a factor 30 on a significant set of data.

An improved algorithm for generalized comparison of minisatellites

Abstract One of the most important objects in genetic mapping and forensic studies are minisatellites. They consist of a heterogeneous tandem array of short repeat units called variants. The evolution of minisatellites is realized by tandem duplication and tandem deletion of variants. Jeffrey et al. proposed a method to obtain the sequence of variants, called maps. Berard and Rivals designed the first algorithm of comparison of two minisatellite maps under an evolutionary model including deletion, insertion, mutation, amplification and contraction. The complexity of this first algorithm was O ( n 4 ) in time and O ( n 3 ) in space where n is the size of the maps. In this paper we propose a more efficient algorithm using the same generic evolutionary model which is O ( n 3 ) in time and O ( n 2 ) in space. Our algorithm with this better efficiency can even solve generalized and more refined models.

On the Transformation Distance Problem

Evolution acts in several ways on biological sequences: either by mutating an element, or by inserting, deleting or copying a segment of the sequence. Varre et al. [12] defined a transformation distance for the sequences, in which the evolutionary operations are copy, reverse copy and insertion of a segment. They also proposed an algorithm to calculate the transformation distance. This algorithm is O(n 4) in time and O(n 4) in space, where n is the size of the sequences. In this paper, we propose an improved algorithm which costs O(n 2) in time and O(n) in space. Furthermore, we extend the operation set by adding deletions. We present an algorithm which is O(n 3) in time and O(n) in space for this more general model.

Alignment of Minisatellite Maps: A Minimum Spanning Tree based Approach

In addition to the well-known edit operations, the alignment of minisatellite maps includes duplication events. We model these duplications using a special kind of spanning trees and deduce an optimal duplication scenario by computing the respective minimum spanning tree. Based on best duplication scenarios for all substrings of the given sequences, we compute an optimal alignment of two minisatellite maps. Our algorithm improves upon the previously developed algorithms in the generality of the model, in alignment quality and in space-time efficiency. Using this algorithm, we derive evidence that there is a directional bias in the growth of minisatellites of the MSY1 dataset.