Constrained Edit Distance Research Articles

New dissimilarity measure for recognizing noisy subsequence trees

Tree is a data structure used to express various objects such as semistructured data and genes. When objects are represented as trees, computing tree similarity is essential for pattern recognition and retrieval. This paper considers the noisy subsequence tree recognition problem whose purpose is to recognize the original tree, given its noisy subsequence tree. Previous research on this problem relied on constrained tree edit distance to measure the dissimilarity. However, the number of relabelings must be predetermined to compute it. This paper proposes a new dissimilarity measure for this problem. Our dissimilarity measure is obtained by counting the node edit operations included in the unit-cost tree edit distance that contribute to the matching of node labels. The number of relabelings need not be specified to compute our dissimilarity measure. Moreover, our measure achieves more accurate recognition performance and faster execution speed than the constrained tree edit distance. Our measure is also useful to solve the tree inclusion problem which is the problem of deciding whether a tree includes another tree and shows the extent of approximate tree inclusion when a tree incompletely includes another tree. © 2011 Wiley Periodicals, Inc. (An early version of this work was presented at the 8th International Conference on Intelligent Data Engineering and Automated Learning (IDEAL'07), Springer LNCS, Vol. 4881, pp. 643–652, 2007.)

A constrained edit distance algorithm between semi-ordered trees

In this paper, we propose a formal definition of a new class of trees called semi-ordered trees and a polynomial dynamic programming algorithm to compute a constrained edit distance between such trees. The core of the method relies on a similar approach to compare unordered [Kaizhong Zhang, A constrained edit distance between unordered labeled trees, Algorithmica 15 (1996) 205–222] and ordered trees [Kaizhong Zhang, Algorithms for the constrained editing distance between ordered labeled trees and related problems, Pattern Recognition 28 (3) (1995) 463–474]. The method is currently applied to evaluate the similarity between architectures of apple trees [Vincent Segura, Aida Ouangraoua, Pascal Ferraro, Evelyne Costes, Comparison of tree architecture using tree edit distances: Application to two-year-old apple tree, Euphytica 161 (2007) 155–164].

A new constrained edit distance between quotiented ordered trees

In this paper we propose a dynamic programming algorithm to compare two quotiented ordered trees using a constrained edit distance. An ordered tree is a tree in which the left-to-right order among siblings is significant. A quotiented ordered tree is an ordered tree T with an equivalence relation on vertices and such that, when the equivalence classes are collapsed to super-nodes, the graph so obtained is an ordered tree as well. Based on an algorithm proposed by Zhang and Shasha [K. Zhang, D. Shasha, Simple fast algorithms for the editing distance between trees and related problems, SIAM Journal on Computing 18 (6) (1989) 1245–1262] and introducing new notations, we describe a tree edit distance between quotiented ordered trees preserving equivalence relations on vertices during computation which works in polynomial time. Its application to RNA secondary structures comparison is finally presented.

FPGA for pseudorandom generator cryptanalysis

FPGAs have been successfully applied for cryptanalytic purposes, particularly in exhaustive key search that is a highly parallelizable task. In this work, we consider a pseudorandom generator scheme that consists of a number of subgenerators, the first of which is a linear feedback shift register (LFSR). LFSR is often used in cipher systems because of good cryptographic characteristics of its output sequence. The cryptanalysis has shown that if noisy prefix of the output sequence of this generator is known, it is possible to reconstruct the initial state of the LFSR by means of generalized correlated attack. The attack is based on the resolving of the constrained edit distance between the sequences determined by the initial states of the shift registers and the intercepted noisy output sequence. The systolic array architecture exploits the intrinsic parallelism of the dynamic programming algorithm for edit distance computation and achieve reductions in computation time of several orders of magnitude comparing with sequential calculation that is characteristic for software solutions. With a minimum increase of area, our design doubles the speed of similar approaches that are applied in bioinformatics, since there are no published ones for cryptanalysis. The obtained results on Xilinx Virtex and Virtex2 FPGA families also holds when a bus is connected, since our design takes into account the bus I/O bottleneck (i.e. PCI).

An Edit Distance between Quotiented Trees

In this paper we propose a dynamic programming algorithm to compare two quotiented trees using a constrained edit distance. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on an adaptation of an algorithm recently proposed by Zhang for comparing unordered rooted trees. This method is currently being used in plant architecture modelling to quantify different types of variability between plants represented by quotiented trees.

The normalized string editing problem revisited

Marzal and Vidal (1993) considered the problem of computing the normalized edit distance between two strings, and reported experimental results which demonstrated the use of the measure to recognize hand-written characters. Their paper formulated the theoretical properties of the measure and developed two algorithms to compute it. In this short communication the authors demonstrate how this measure is related to an auxiliary measure already defined in the literature-the inter-string constrained edit distance. Since the normalized edit distance can be computed efficiently using the latter, the analytic and experimental results reported in the above paper can be obtained just as accurately, but more efficiently, using the strategies presented here.

A constrained edit distance between unordered labeled trees

This paper considers the problem of computing a constrained edit distance between unordered labeled trees. The problem of approximate unordered tree matching is also considered. We present dynamic programming algorithms solving these problems in sequential timeO(|T1|×|T2|×(deg(T1)+deg(T2))× log2(deg(T1)+deg(T2))). Our previous result shows that computing the edit distance between unordered labeled trees is NP-complete.

A Constrained Edit Distance Between Unordered Labeled Trees

A Constrained Edit Distance Between Unordered Labeled Trees

Constrained many-to-one string editing with memory

A new constrained edit distance between an ordered set of input strings and a single output string is proposed, where all the strings are over a finite alphabet. Editing transformation includes deletion of symbols from the input strings, combination of the decimated input strings by a function with memory, and substitution and insertion of symbols in the combination string. Constraints are related to the total number of edit operations and to the maximum numbers of consecutive deletions and insertions. A recursive algorithm for efficient computation of the constrained edit distance is derived and its computational complexity is determined. Potential applications in cryptanalysis of shift-register-based stream ciphers and in decoding for parallel communication channels with synchronization errors are also discussed.

Recognition of Noisy Subsequences Using Constrained Edit Distances

Let X* be any unknown word from a finite dictionary H. Let U be any arbitrary subsequence of X*. We consider the problem of estimating X* by processing Y, which is a noisy version of U. We do this by defining the constrained edit distance between XH and Y subject to any arbitrary edit constraint involving the number and type of edit operations to be performed. An algorithm to compute this constrained edit distance has been presented. Although in general the algorithm has a cubic time complexity, within the framework of our solution the algorithm possesses a quadratic time complexity. Recognition using the constrained edit distance as a criterion demonstrates remarkable accuracy. Experimental results which involve strings of lengths between 40 and 80 and which contain an average of 26.547 errors per string demonstrate that the scheme has about 99.5 percent accuracy.