fast algorithms for computing tree lcs the lcs of two rooted ordered and labeled trees f and g is the largest forest that can be obtained from both trees by deleting nodes we present algorithms for computing tree lcs which exploit the sparsity inherent to the tree lcs problem assuming g is smaller than f our first algorithm runs in time o email protected height f height g lglg g where r is the number of pairs email protected f email protected g such that v and w have the same label our second algorithm runs in time o email protected lglg g where l is the size of the lcs of f and g for this algorithm we present a novel three dimensional alignment graph our third algorithm is intended for the constrained variant of the problem in which only nodes with zero or one children can be deleted for this case we obtain an o rhlglg g time algorithm where h height f height g

kernelization and parameterized algorithms for covering a tree by a set of stars or paths two restricted versions of the subforest isomorphism problem the covering a tree by a set of stars ctss and the covering a tree by a set of paths ctsp problems are studied both problems are np complete the problems are closely related to a number of well studied problems including the problems subgraph isomorphism tree editing and graph packing it is shown that the problems ctss and ctsp are fixed parameter tractable thorough development of parameterized algorithms and kernelization algorithms for these problems are presented

finding similar consensus between trees an algorithm and a distance hierarchy abstract the problem of finding this similar consensus also known as the largest approximately common substructures of two trees arises in many pattern recognition applications this paper presents a dynamic programming algorithm to solve the problem based on the distance measure originated from tanaka and tanaka the algorithm runs as fast as the best known algorithm for comparing two trees using tanaka s distance measure when the allowed distance between the common substructures is a constant independent of the input trees in addition we establish a hierarchy among tanaka s distance measure and three other edit based distance measures published in the literature

bayesian graph edit distance this paper describes a novel framework for comparing and matching corrupted relational graphs the paper develops the idea of edit distance originally introduced for graph matching by sanfeliu and fu 1983 we show how the levenshtein distance 1966 can be used to model the probability distribution for structural errors in the graph matching problem this probability distribution is used to locate matches using map label updates we compare the resulting graph matching algorithm with that recently reported by wilson and hancock the use of edit distance offers an elegant alternative to the exhaustive compilation of label dictionaries moreover the method is polynomial rather than exponential in its worst case complexity we support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem this demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

on the similarity metric and the distance metric similarity and dissimilarity measures are widely used in many research areas and applications when a dissimilarity measure is used it is normally required to be a distance metric however when a similarity measure is used there is no formal requirement in this article we have three contributions first we give a formal definition of similarity metric second we show the relationship between similarity metric and distance metric third we present general solutions to normalize a given similarity metric or distance metric

average complexity of the jiang wang zhang pairwise tree alignment algorithm and of a rna secondary structure alignment algorithm we prove that the average complexity of the pairwise ordered tree alignment algorithm of jiang wang and zhang is in o nm where n and m stand for the sizes of the two trees respectively we show that the same result holds for the average complexity of pairwise comparison of rna secondary structures using a set of biologically relevant operations

hierarchical inference of unicast network topologies based on end to end measurements in this paper we address the problem of topology discovery in unicast logical tree networks using end to end measurements without any cooperation from the internal routers topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pairwise correlations as similarity metrics unlike previous work that first assumes the network topology is a binary tree and then tries to generalize to a nonbinary tree we provide a framework that directly deals with general logical tree topologies a hierarchical algorithm to estimate the topology is developed in a recursive manner by finding the best partitions of the leaf nodes level by level our simulations show that the algorithm is more robust than binary tree based methods

brief paper some properties of the output error method the output error identification method is studied in various respects the stationary points of the associated loss function are investigated sufficient conditions for a unique local minimum are given the loss functions can be minimized using a quasilinearization algorithm such an algorithm will give good local convergence it is however shown that global convergence does not always occur the output error method is also compared with some other estimation methods from the accuracy point of view it is proved that a prediction error method will give better accuracy an instrumental variable technique may give better or worse accuracy depending on the actual noise correlation

computing similarity between rna structures the primary structure of a ribonucleic acid rna molecule is a sequence of nucleotides bases over the four letter alphabet a c g u the secondary or tertiary structure of an rna is a set of base pairs nucleotide pairs which forms bonds between au and cg for secondary structures these bonds have been traditionally assumed to be one to one and non crossing this paper considers a notion of similarity between two rna molecule structures taking into account the primary the secondary and the tertiary structures we show that for tertiary structures it is max snp hard for both minimization and maximization versions we show a stronger result for the maximization version where it cannot be approximated within ratio 2logn in polynomial time unless npdtime 2polylogn we then present an algorithm that can be used for practical application our algorithm will produce an optimal solution for the case where at least one of the rna involved is of a secondary structure we also show an approximation algorithm

alignment distance of regular tree languages abstract we consider the tree alignment distance problem between a tree and a regular tree language the tree alignment distance is an alternative of the tree edit distance in which we construct an optimal alignment between two trees and compute its cost instead of directly computing the minimum cost of tree edits the alignment distance is crucial for understanding the structural similarity between trees we in particular consider the following problem given a tree t and a tree automaton recognizing a regular tree language l find the most similar tree from l with respect to t under the tree alignment metric regular tree languages are commonly used in practice such as xml schema or bioinformatics we propose an o m n time algorithm for computing the ordered alignment distance between t and l when the maximum degree of t and trees in l is bounded by a constant and o m n 2 time algorithm when the maximum degree of trees in l is not bounded where m is the size of t and n is the size of a finite tree automaton for l we also study the case where a tree is not necessarily ordered and show that the time complexity remains o m n if the maximum degree is bounded and max snp hard otherwise

symmetry methods and space group representations in the theory of phase transitions abstract a review is presented of main results of the phenomenological theory of phase transitions obtained by means of irreducible representations ir of the space symmetry groups a geometrical method for obtaining low symmetry phases as well as a scheme of a thermodynamical analysis of phase transitions consistent with this method are described basic principles are expounded of construction and analysis of the phase diagrams for multicomponent order parameters it has been established that even if the lifshitz condition is satisfied there may be some symmetry related reasons giving rise to incommensurate phases near the multicritical point phase diagrams are presented typical of this case the role of external symmetry breaking fields has been analyzed it has been shown on the basis of the general symmetry principles that a certain domain structure may exist on an ideal crystal surface the structure of low symmetry phases has been described using the notion of complete condensate of order parameters a connection between this approach and that based on the theory of color symmetry has been discussed

an algebraic view of the relation between largest common subtrees and smallest common supertrees the relationship between two important problems in tree pattern matching the largest common subtree and the smallest common supertree problems is established by means of simple constructions which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them and vice versa these constructions are the same for isomorphic homeomorphic topological and minor embeddings they take only time linear in the size of the trees and they turn out to have a clear algebraic meaning

constrained tree editing the distance between two ordered labeled trees is considered to be the minimum sum of the weights associated with the edit operations insertion deletion and substitution required to transform one tree to another the problem of computing this distance and the optimal transformation using no edit constraints has been studied in the literature 3 4 7 9 111 in this paper we consider the problem of transforming one tree t1 to another tree t2 using any arbitrary edit constraint involving the number and type of edit operations to be performed an algorithm to compute this constrained distance is presented if for a tree t span t is defined as the min depth t leaves t the time and space complexities of this algorithm are

identifying consensus of trees through alignment abstract in this paper we present a dynamic programming algorithm for identifying the similar consensus sc or the largest approximately common substructures of two ordered labeled trees based on the alignment distance we consider a substructure of a tree t to be a connected subgraph of t given two trees t 1 t 2 and an integer d the sc problem is to find a substructure u 1 of t 1 and a substructure u 2 of t 2 such that u 1 is within distance d of u 2 and where there does not exist any other substructure v 1 of t 1 and v 2 of t 2 such that v 1 and v 2 satisfy the distance constraint and the sum of the sizes of v 1 and v 2 is greater than the sum of the sizes of u 1 and u 2 the proposed algorithm solves the sc problem in time o d 2 t 1 t 2 g 1 g 2 2 where t i i 1 2 is the size of tree t i and g i is the maximum degree of t i this is as fast as the best known algorithm for aligning two ordered labeled trees when the distance allowed in the common substructures is a constant independent of the input trees to demonstrate the utility of our algorithm we discuss its application to characterizing the conformation space of rna sequences pertaining to the poliovirus human rhinovirus and coxsackievirus where the rna structures are represented by ordered labeled trees

adaptive algorithms for constrained arma signals in the presence of noise a family of algorithms is developed for adaptive parameter estimation of constrained autoregressive moving average arma signals in the presence of noise these algorithms utilize a priori information about the signal s properties such as its spectral type for example low pass bandpass etc or a spatial domain characteristic special applications include modeling of autoregressions ar and signals of known spectral type in the presence of noise signal deconvolution image deblurring and multipath parameter estimation selected results of simulations are included to demonstrate the performance of the algorithms

relation between multidimensional representations of the fedorov groups and the groups of color symmetry abstract relations have been traced between multidimensional irreducible representations ir of the fedorov groups and the groups of color symmetry using as an example the phase transitions in crystals unlike the case of the one dimensional real ir s for which the indenbom niggli theorem is valid for the multidimensional ir s a one to one relationship between them and the color symmetry groups is disturbed namely each multidimensional ir of the fedorov group is associated not with one but rather with a whole set of the color symmetry groups and conversely each group of the color symmetry is associated not with one ir but with a certain set of these complete correspondence between the color symmetry groups and the ir s of the fedorov group can be established on the basis of an analysis of the complete condensate of order parameters it has been shown that on the set of different domains of a low symmetry phase macroscopic level there are acting certain p symmetry groups when however the structure of one domain of such a phase microscopic level is described the w p symmetry groups have to be used the distinguishing feature of the w p symmetry as compared to the p symmetry is this each element of the classical group is assigned not one color permutation but different permutations depending on which point of the space is subjected to the action of this element it has also been shown that to the w p symmetry groups describing the structure of one domain there corresponds generally speaking nonrectangular young diagrams

adaptive parameter estimation for a constrained low pass system a novel algorithm is presented for adaptive parameter estimation for a constrained low pass butterworth system model the algorithm will estimate the system cutoff frequency and gain online when it is known that the true system has a low pass butterworth structure or some transfer function similar to it and its true order is used the algorithm will lead to a substantial savings in computation and more accurate results than unconstrained algorithms potential applications include filter design and adaptive decision on nyquist rate for systems

forest alignment with affine gaps and anchors applied in rna structure comparison we present two enhancements to jiang s tree alignment algorithm motivated by experience with its use for rna structure alignment one enhancement is the introduction of an affine gap model which can be accommodated with a runtime increase by a constant factor the second enhancement is a speed up of the alignment algorithm when certain nodes in the trees are pre aligned by a so called anchoring both enhancements are included in a new implementation of the tool rnaforester we evaluate the new algorithm with two applications related to rna secondary structure analysis based on our experience we suggest a new formulation of the tree alignment model based on regular tree languages and rewrite rules

adaptive pole estimation an adaptive algorithm is developed for online estimation of the poles of autoregressive ar processes the method estimates the poles directly from the data without intermediate estimation of the ar coefficients or polynomial factorization it converges rapidly is computationally efficient and attains the cramer rao bound crb asymptotically a closed form expression for the asymptotic crb is provided convergence to the true solution is proved and methods are discussed for extending the algorithm for use with more general e g autoregressive moving average models numerical examples are presented to demonstrate the performance of the algorithm

an algorithm for finding the largest approximately common substructures of two trees ordered labeled trees are trees in which each node has a label and the left to right order of its children if it has any is fixed such trees have many applications in vision pattern recognition molecular biology and natural language processing we consider a substructure of an ordered labeled tree t to be a connected subgraph of t given two ordered labeled trees t sub 1 and t sub 2 and an integer d the largest approximately common substructure problem is to find a substructure u sub 1 of t sub 1 and a substructure u sub 2 of t sub 2 such that u sub 1 is within edit distance d of u sub 2 and where there does not exist any other substructure v sub 1 of t sub 1 and v sub 2 of t sub 2 such that v sub 1 and v sub 2 satisfy the distance constraint and the sum of the sizes of v sub 1 and v sub 2 is greater than the sum of the sizes of u sub 1 and u sub 2 we present a dynamic programming algorithm to solve this problem which runs as fast as the fastest known algorithm for computing the edit distance of two trees when the distance allowed in the common substructures is a constant independent of the input trees to demonstrate the utility of our algorithm we discuss its application to discovering motifs in multiple rna secondary structures which are ordered labeled trees

selected tree classifier combination based on both accuracy and error diversity this paper proposes a method for combining multiple tree classifiers based on both classifier ensemble bagging and dynamic classifier selection schemes dcs the proposed method is composed of the following procedures 1 building individual tree classifiers based on bootstrap samples 2 calculating the distance between all possible two trees 3 clustering the trees based on single linkage clustering 4 selecting two clusters by local region in terms of accuracy and error diversity and 5 voting the results of tree classifiers selected in the two clusters empirical evaluation using publicly available data sets confirms the superiority of our proposed approach over other classifier combining methods

approximation and parameterized algorithms for common subtrees and edit distance between unordered trees given two rooted labeled unordered trees the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship the tree edit distance problem is to determine the least cost sequence of insertions deletions and substitutions that converts a tree into another given tree both problems are known to be hard to approximate within some constant factor in general we tackle these problems from two perspectives giving exact algorithms either for special cases or in terms of some parameters and approximation algorithms and hardness of approximation we present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees this is complemented with a tighter apx hardness proof that holds when the trees are of height one and two respectively furthermore we present the first approximation algorithms for both problems in particular for the common subtree problem for t trees we present an algorithm achieving a tlog 2 b o p t 1 ratio where b o p t is the number of branching nodes in the optimal solution we also present constant factor approximation algorithms for both problems in the case of bounded height trees

a metric for rooted trees with unlabeled vertices based on nested parentheses in this paper we propose a new metric for rooted trees with unlabeled vertices based on alignments of nested parenthesis strings we prove that the time complexity for computing this metric is np hard and present a 1 5 approximation algorithm for it

polynomial time metrics for attributed trees we address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree the proposed measures are general and defined on trees endowed with either symbolic or continuous valued attributes and can be applied to rooted as well as unrooted trees we prove that our measures satisfy the metric constraints and provide a polynomial time algorithm to compute them this is a remarkable and attractive property since the computation of traditional edit distance based metrics is in general np complete at least in the unordered case we experimentally validate the usefulness of our metrics on shape matching tasks and compare them with an approximation of edit distance

a new algorithm for aligning nested arc annotated sequences under arbitrary weight schemes in this paper we propose a new algorithm for the alignment of nested arc annotated sequences having applications in the comparison of rna secondary structures without pseudo knots we use a general edit distance model between arc annotated sequences that considers classical sequences of edit operations and structural edit operations on arcs in this model the general edit distance problem under a non constrained weight scheme is np hard recently a hierarchy of arc annotated sequence alignment problems that highlights less general but tractable problems was introduced we refine this hierarchy of alignment problems and extend the class of tractable alignment problems up to date the alignment problem we solve is the most general one that is known to be tractable in the considered edit distance model and under arbitrary weight schemes this algorithm is efficient as its asymptotic time and space complexities are the same as the complexities of the best previously published algorithm

a new algorithm for computing similarity between rna structures abstract the primary structure of a ribonucleic acid rna molecule is a sequence of nucleotides bases over the four letter alphabet a c g u the secondary or tertiary structure of an rna is a set of base pairs nucleotide pairs which form bonds between a u and c g for secondary structures these bonds have been traditionally assumed to be one to one and non crossing we consider the edit distance between two rna structures this is a notion of similarity introduced in proceedings of the tenth symposium on combinatorial pattern matching lecture notes in computer science vol 1645 springer berlin 1999 p 281 between two rna molecule structures taking into account the primary the secondary and the tertiary structures in general this problem is np hard for tertiary structures in this paper we consider this notion under some constraints we present an algorithm and then show how to use this algorithm for practical applications

design variables for bias distribution in transfer function estimation estimation of transfer functions of linear systems is one of the most common system identification problems several different design variables chosen by the user for the identification procedure affect the properties of the resulting estimate in this paper it is investigated how the choices of prefilters noise models sampling interval and prediction horizon i e the use of k step ahead prediction methods influence the estimate an important aspect is thai the true system is not assumed to be exactly represented within the chosen model set the estimate will thus be biased it is shown how the distribution of bias in the frequency domain is governed by a weighting function which emphasizes different frequency bands the weighting function in turn is a result of the previously listed design variables it is shown e g thai the common least squares method has a tendency to emphasize high frequencies and that this can be counteracted by prefiltering it is also shown that asymptotically it is only the prediction horizon itself and not how it is split up into sampling interval times number of predicted sampling instants that affects this weighting function

alignment of trees an alternative to tree edit abstract in this paper we propose the alignment of trees as a measure of the similarity between two labeled trees both ordered and unordered trees are considered an algorithm is designed for ordered trees the time complexity of this algorithm is o t 1 t 2 deg t 1 deg t 2 2 where t 1 is the number of nodes in t 1 and deg t 1 is the degree of t 1 i 1 2 the algorithm is faster than the best known algorithm for tree edit when deg t 1 and deg t 2 are smaller than the depths of t 1 and t 2 for unordered trees we show that the alignment problem can be solved in polynomial time if the trees have a bounded degree and becomes max snp hard if one of the trees is allowed to have an arbitrary degree in contrast the edit problem for unordered trees is max snp hard even if both trees have a bounded degree zhang and jiang 1994 finally multiple alignment of trees is discussed

simple fast algorithms for the editing distance between trees and related problems ordered labeled trees are trees in which the left to right order among siblings is significant the distance between two ordered trees is considered to be the weighted number of edit operations insert delete and modify to transform one tree to another the problem of approximate tree matching is also considered specifically algorithms are designed to answer the following kinds of questions 1 what is the distance between two trees 2 what is the minimum distance between t 1 and t 2 when zero or more subtrees can be removed from t 2 3 let the pruning of a tree at node n mean removing all the descendants of node n the analogous question for prunings as for subtrees is answered a dynamic programming algorithm is presented to solve the three questions in sequential time o t 1 times t 2 times min textit depth t 1 textit leaves t 1 times min textit depth t 2 textit leaves t 2 and space o t 1 times t 2 compared with o t 1 times t 2 t

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

image categorization graph edit distance edge direction histogram this paper presents a novel algorithm for computing graph edit distance ged in image categorization this algorithm is purely structural i e it needs only connectivity structure of the graph and does not draw on node or edge attributes there are two major contributions 1 introducing edge direction histogram edh to characterize shape features of images it is shown that ged can be employed as distance of edhs this algorithm is completely independent on cost function which is difficult to be defined exactly 2 computing distance of edhs with earth mover distance emd which takes neighborhood bins into account so as to compute distance of edhs correctly a set of experiments demonstrate that the newly presented algorithm is available for classifying and clustering images and is immune to the planar rotation of images compared with ged from spectral seriation our algorithm can capture the structure change of graphs better and consume 12 79 time used by the former one the average classification rate is 5 and average clustering rate is 25 higher than the spectral seriation method

identifying approximately common substructures in trees based on a restricted edit distance in this paper we present a dynamic programming algorithm for identifying the largest approximately common substructures lacss of two ordered labeled trees we consider a substructure of a tree t to be a connected subgraph of t given two trees t1 t2 and an integer d the lacs problem is to find a substructure u1 of t1 and a substructure u2 of t2 such that u1 is within distance d of u2 and where there does not exist any other substructure v1 of t1 and v2 of t2 such that v1 and v2 satisfy the distance restriction and the sum of the sizes of v1 and v2 is greater than the sum of the sizes of u1 and u2 the distance measure considered in the paper is a restricted edit distance originated from selkow the lacs problem is motivated by the studies of program and document comparison the proposed algorithm solves the problem in time o d2 t1 t2 which is as fast as the best known algorithm for calculating selkow s distance of two trees when the distance allowed in the common substructures is a constant independent of the input trees

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

a similarity measure for graphs with low computational complexity we present and analyze an algorithm to measure the structural similarity of generalized trees a new graph class which includes rooted trees for this we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings we prove that the obtained graph similarity measures are so called backward similarity measures from this we find that the time complexity of our algorithm is polynomial and hence significantly better than the time complexity of classical graph similarity methods based on isomorphic relations