An efficient algorithm for sequence comparison with block reversals

AbstractGiven two sequences X and Y that are strings over some alphabet set, we consider the distance d(X,Y) between them defined to be minimum number of character replacements and block (substring) reversals needed to transform X to Y (or vice versa). The operations are required to be disjoint. This is the “simplest” sequence comparison problem we know of that allows natural block edit operations. Block reversals arise naturally in genomic sequence comparison; they are also of interest in matching music data. We present an algorithm for exactly computing the distance d(X,Y); it takes time O(|X|log2|X|), and hence, is near-linear. Trivial approach takes quadratic time

Parking functions, labeled trees and DCJ sorting scenarios

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure

Online Pattern Matching for String Edit Distance with Moves

Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string to the other. Although optimizing EDM is intractable, it has many applications especially in error detections. Edit sensitive parsing (ESP) is an efficient parsing algorithm that guarantees an upper bound of parsing discrepancies between different appearances of the same substrings in a string. ESP can be used for computing an approximate EDM as the L1 distance between characteristic vectors built by node labels in parsing trees. However, ESP is not applicable to a streaming text data where a whole text is unknown in advance. We present an online ESP (OESP) that enables an online pattern matching for EDM. OESP builds a parse tree for a streaming text and computes the L1 distance between characteristic vectors in an online manner. For the space-efficient computation of EDM, OESP directly encodes the parse tree into a succinct representation by leveraging the idea behind recent results of a dynamic succinct tree. We experimentally test OESP on the ability to compute EDM in an online manner on benchmark datasets, and we show OESP's efficiency.Comment: This paper has been accepted to the 21st edition of the International Symposium on String Processing and Information Retrieval (SPIRE2014

On Weighting Schemes for Gene Order Analysis

Gene order analysis aims at extracting phylogenetic information from the comparison of the order and orientation of the genes on the genomes of different species. This can be achieved by computing parsimonious rearrangement scenarios, i.e. to determine a sequence of rearrangements events that transforms one given gene order into another such that the sum of weights of the included rearrangement events is minimal. In this sequence only certain types of rearrangements, given by the rearrangement model, are admissible and weights are assigned with respect to the rearrangement type. The choice of a suitable rearrangement model and corresponding weights for the included rearrangement types is important for the meaningful reconstruction. So far the analysis of weighting schemes for gene order analysis has not been considered sufficiently. In this paper weighting schemes for gene order analysis are considered for two rearrangement models: 1) inversions, transpositions, and inverse transpositions; 2) inversions, block interchanges, and inverse transpositions. For both rearrangement models we determined properties of the weighting functions that exclude certain types of rearrangements from parsimonious rearrangement scenarios

GNSS signal acquisition in the presence of sign transitions

The next generation of Global Navigation Satellite Systems (GNSS), such as Galileo [1] and GPS modernization [2], will use signals with equal code and bit periods, which will introduce a potential sign transition in each segment of the signal processed in the acquisition block. If FFT is used to perform the correlations a sign transition occurring within the integration time may cause a splitting of the main peak of the Cross Ambiguity Function (CAF) into two smaller lobes along the Doppler shift axis [3]. In this paper a method to overcome the possible impairments due to the lobe splitting is proposed and validated by simulatio