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

an efficient strategy for generating all descendant subtree patterns from phylogenetic trees with its implementation abstract phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we efficiently solve two subtree comparison problems on a set of phylogenetic trees which have practical applications to analyze the evolution and co evolution genes clustering of genomic sequences let t 1 t 2 t k be a set of k phylogenetic trees such that the leaves of each tree are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same where n is the maximum number of the leaves among the k trees we present a linear time algorithm to find all the leaf agreement descendant subtrees by further extending this result we present a linear time algorithm to find all the leaf agreement isomorphic descendant subtrees based on our algorithms a web based system using input tree files from treebase is also implemented

fast comparison of evolutionary trees abstract constructing evolutionary trees for species sets is a fundamental problem in biology unfortunately there is no single agreed upon method for this task and many methods are in use current practice dictates that trees be constructed using different methods and that the resulting trees then be compared for consensus it has become necessary to automate this process as the number of species under consideration has grown we study the unrooted maximum agreement subtree problem umast and its rooted variant rmast the umast problem is as follows given a set a and two trees t 0 and t 1 leaf labeled by the elements of a find a maximum cardinality subset b of a such that the restrictions of t 0 and t 1 to b are topologically isomorphic our main result is an o n 2 o 1 time algorithm for the umast problem we also derive an o n 2 time algorithm for the rmast problem the previous best algorithm for both these problems has running time o n 4 5 o 1

limits of space times in five dimensions and their relation to the segre types a limiting diagram for the segre classification in 5 dimensional space times is obtained extending a recent work on limits of the energy momentum tensor in general relativity some of geroch s results on limits of space times in general relativity are also extended to the context of five dimensional kaluza klein space times

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

algorithms for approximate graph matching abstract labeled graphs are graphs in which each node and edge has a label the distance between two labeled graphs is considered to be the weighted sum of the costs of edit operations insert delete and relabel the nodes and edges to transform one graph to the other the paper considers two variants of the approximate graph matching problem agm given a pattern graph p and a data graph d 1 1 what is the distance between p and d 2 2 what is the minimum distance between p and d when subgraphs can be freely removed from d we first show that no efficient algorithm can solve either variant of the agm unless p np then we present several heuristic algorithms leading to approximate solutions the heuristics are based on probabilistic hill climbing and maximum flow techniques our experimental results involving the comparison of real and simulated data demonstrate the good performance of the algorithms 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

ordered and unordered tree inclusion the following tree matching problem is considered given labeled trees p and t can p be obtained from t by deleting nodes deleting a node u entails removing all edges incident to u and if u has a parent v replacing the edge from v to u by edges from v to the children of u the problem is motivated by the study of query languages for structured text databases simple solutions to this problem require exponential time for ordered trees an algorithm is presented that requires o p t time and space the corresponding problem for unordered trees is also considered and a proof of its np completeness is given an algorithm is presented for the unordered problem this algorithm works in o p t time if the out degrees of the nodes in p are bounded by a constant and in polynomial time if they are o log t

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

space average and wave interference in vibration conductivity plane wave interference and space averages play a significant role in the derivation of some vibration conductivity equations that are becoming more and more popular in modelling vibroacoustic problems particularly the thermal approach and the modified vibration conductivity equations are here considered with the aim of establishing similarities and or differences between them and stating relevant consequences it is shown by formal developments that the thermal equation is obtained under the assumption of performing appropriate space averages while the modified vibration conductivity equation does not need in some cases this condition it is discussed however that in practical applications the conditions of validity of both approaches are quite similar

graph embedding using tree edit union in this paper we address the problem of how to learn a structural prototype that can be used to represent the variations present in a set of trees the prototype serves as a pattern space representation for the set of trees to do this we construct a super tree to span the union of the set of trees this is a chicken and egg problem since before the structure can be estimated correspondences between the nodes of the super tree and the nodes of the sample tree must be to hand we demonstrate how to simultaneously estimate the structure of the super tree and recover the required correspondences by minimizing the sum of the tree edit distances over pairs of trees subject to edge consistency constraints each node of the super tree corresponds to a dimension of the pattern space and for each tree we construct a pattern vector in which the elements of the weights corresponding to each of the dimensions of the super tree we perform pattern analysis on the set of trees by performing principal components analysis on the vectors the method is illustrated on a shape analysis problem involving shock trees extracted from the skeletons of 2d objects

on finding the adams consensus tree abstract this article presents a fast algorithm for finding the adams consensus tree of a set of conflicting phylogenetic trees with identical leaf labels its worst case running time is o k n log n where k is the number of input trees and n is the size of the leaf label set in comparison the original algorithm of adams has a worst case running time of o k n 2 to achieve subquadratic running time the centroid path decomposition technique is applied in a novel way that traverses the input trees by following a centroid path in each of them in unison for k 2 an even faster algorithm running in o n log n log log n time is provided which relies on an extension of the wavelet tree based technique of bose et al for orthogonal range counting on a grid our extended wavelet tree data structure also supports truncated range maximum minimum queries efficiently

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

on the pattern recognition of noisy subsequence trees we consider the problem of recognizing ordered labeled trees by processing their noisy subsequence trees which are patched up noisy portions of their fragments we assume that h a finite dictionary of ordered labeled trees is given x is an unknown element of h and u is any arbitrary subsequence tree of x we consider the problem of estimating x by processing y which is a noisy version of u the solution which we present is to our knowledge the first reported solution to the problem we solve the problem by sequentially comparing y with every element x of h the basis of comparison being a new dissimilarity measure between two trees which implicitly captures the properties of the corrupting mechanism that noisily garbles u into y the algorithm which incorporates this constraint has been used to test our pattern recognition system and the experimental results obtained demonstrate good accuracy

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

on the complexity of finding a largest common subtree of bounded degree the largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship the problem is known to be np hard for unordered trees in this paper we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant d we present an o nd time algorithm where n is the maximum size of two input trees which improves a previous o n2d time algorithm we also present an o h222h1d2h d1poly n time algorithm where h is the maximum height of two input trees

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

finding common structured patterns in linear graphs a linear graph is a graph whose vertices are linearly ordered this linear ordering allows pairs of disjoint edges to be either preceding nesting or crossing given a family of linear graphs and a non empty subset email protected we are interested in the maximum common structured pattern mcsp problem find a maximum size edge disjoint graph with edge pairs all comparable by one of the relations in r that occurs as a subgraph in each of the linear graphs of the family the mcsp problem generalizes many structure comparison and structure prediction problems that arise in computational molecular biology we give tight hardness results for the mcsp problem for structured patterns and structured patterns furthermore we prove that the problem is approximable within ratios i email protected k for structured patterns ii k 1 2 for structured patterns and iii o klogk for structured patterns where k is the size of the optimal solution and k email protected i 1 k1 i is the kth harmonic number also we provide combinatorial results concerning different types of structured patterns that are of independent interest in their own right

sparse dynamic programming for evolutionary tree comparison constructing evolutionary trees for species sets is a fundamental problem in biology unfortunately there is no single agreed upon method for this task and many methods are in use current practice dictates that trees be constructed using different methods and that the resulting trees should be compared for consensus it has become necessary to automate this process as the number of species under consideration has grown we study one formalization of the problem the maximum agreement subtree mast problem the mast problem is as follows given a set a and two rooted trees ct 0 and ct 1 leaf labeled by the elements of a find a maximum cardinality subset b of a such that the topological restrictions of ct 0 and ct 1 to b are isomorphic in this paper we will show that this problem reduces to unary weighted bipartite matching uwbm with an o n 1 o 1 additive overhead we also show that uwbm reduces linearly to mast thus our algorithm is optimal unless uwbm can be solved in near linear time the overall running time of our algorithm is o n 1 5 log n improving on the previous best algorithm which runs in o n 2 we also derive an o n c sqrt log n time algorithm for the case of bounded degrees whereas the previously best algorithm runs in o n 2 as in the unbounded case

tree contractions and evolutionary trees an evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species evolutionary trees are useful for modeling the evolutionary history of species an agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees we give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees t1 and t2 with n leaves each if the maximum degree d of these trees is bounded by a constant the time complexity is o n log2n and is within a log n factor of optimal for general d this algorithm runs in o nd2 log d log2 n time or alternatively in o nd sqrt d log 3 n time

computing the maximum agreement of phylogenetic networks we introduce the maximum agreement phylogenetic subnetwork problem masn for finding branching structure shared by a set of phylogenetic networks we prove that the problem is np hard even if restricted to three phylogenetic networks and give an o n2 time algorithm for the special case of two level 1 phylogenetic networks where n is the number of leaves in the input networks and where n is called a level f phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of n containing at most f nodes with indegree 2 we also show how to extend our technique to yield a polynomial time algorithm for any two level f phylogenetic networks n1 n2 satisfying f o log n more precisely its running time is o v n1 v n2 2f1 f2 where v ni and fi denote the set of nodes in ni and the level of ni respectively for i 1 2

classification of second order symmetric tensors in five dimensional kaluza klein type theories an algebraic classification of second order symmetric tensors in five dimensional kaluza klein type lorentzian spaces is presented by using jordan matrices it is shown that the possible segre types are 1 1111 2111 311 zz111 and the degeneracies thereof a set of canonical forms for each segre type is found the possible continuous groups of symmetry for each canonical form are also studied

an o n log n algorithm for the maximum agreement subtree problem for binary trees the maximum agreement subtree problem is the following given two rooted trees whose leaves are drawn from the same set of items e g species find the largest subset of these items so that the portions of the two trees restricted to these items are isomorphic we consider the case which occurs frequently in practice i e the case when the trees are binary and give an o nlog n time algorithm for this problem

models of space averaged energetics of plates the analysis of high frequency vibrations of plates is of particular interest for many cases of structure borne noise in aircraft the current methods of analysis are either too expensive finite element method or may have a confidence band wider than desirable statistical energy analysis an alternative technique to model the spaceand time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation transmission and absorption is highly desirable the focus of this paper is the development of a set of equations that govern the space and time averaged energy density in plates to solve this equation a boundary value problem must be considered in terms of energy density variables using energy and intensity boundary conditions a verification study of the energy governing equation is performed a finite element formulation of the new equations is also implemented and several tests cases are analyzed and compared to analytical solutions cg d e e 6j f f h k p q q x w 17 v p

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

finding approximate patterns in undirected acyclic graphs abstract we consider an approximate pattern matching problem for undirected acyclic graphs specifically let p be a pattern graph d a data graph and t an integer we present an algorithm to locate a subgraph in d whose distance from p is at most t the distance measure used here is the degree 2 metric published previously the time complexity of our algorithm is o n p n d d d log d where n p and n d are the number of nodes in p and d respectively d min d p d d d p and d d are the maximum degree of p and d respectively central to our algorithm is a procedure for finding approximate patterns in rooted unordered trees and freely allowing cuts we discuss two applications of the algorithms in chemical information search and website management on the internet

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

maximum agreement subtree in a set of evolutionary trees metrics and efficient algorithms the maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species an agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent under a suitable definition in all given evolutionary trees recently dynamic programming ideas were used to provide polynomial time algorithms for finding a maximum homeomorphic agreement subtree of two trees generalizing these methods to sets of more than two trees yields algorithms that are exponential in the number of trees unfortunately it turns out that in reality one is usually presented with more than two trees sometimes as many as thousands of trees in this paper we prove that the maximum homeomorphic agreement subtree problem is cal np complete for three trees with unbounded degrees we then show an approximation algorithm of time o kn5 for choosing the species that are not in a maximum agreement subtree of a set of k trees our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution while the set of evolutionary trees may be large in practice the trees usually have very small degrees typically no larger than three we develop a new method for finding a maximum agreement subtree of k trees of which one has degree bounded by d this new method enables us to find a maximum agreement subtree in time o knd 1 n2d

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

on the vibrational conductivity approach to high frequency dynamics for two dimensional structural components abstract the vibrational conductivity approach to high frequency dynamics is applied here to the case of two dimensional structural components with this approach an equation which is analogous to the steady state heat conduction equation is used to model the spatial variation of the energy density of the structure it is shown that the standard derivation of the method is incomplete in the sense that the steady state heat conduction equation admits a class of solution which is not encompassed by the assumed form of response and a revised derivation is presented it is further shown that the associated boundary conditions for coupled structural components may be expressed in terms of the coupling loss factors which are used in statistical energy analysis a variational principle for the differential equation and the associated boundary conditions is then derived which permits the application of the rayleigh ritz technique to coupled problems and it is shown that a one term rayleigh ritz solution leads to standard statistical energy analysis the method is applied to a single plate and to two coupled plates and it is found that the technique is unable to provide an accurate estimate of the direct field due to point loading this difficulty is traced to the fact that the assumptions employed in the derivation become self contradictory for this case finally the usefulness or otherwise of the approach as an engineering tool is discussed

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

rna secondary structure comparison exact analysis of the zhang shasha tree edit algorithm we are interested in rna secondary structure comparison using an approach which consists to represent these structures by labeled ordered trees following the problem considered this tree representation can be rough considering only the structural patterns or refined until an exact coding of the structure is obtained after some preliminary definitions and the description of the zhang shasha siam j comput 18 6 1989 1245 tree edit algorithm which is on the one hand the reference when dealing with ordered labeled trees comparison and on the other hand the starting point of our work this article will present an exact analysis of its complexity the purpose of this work is also to lead us to a better comprehension of the parameters of this algorithm in order to be able to modify it more easily without changing its time complexity to take into account biological constraints that occur when comparing rna secondary structures

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

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

a space averaged quadratic method for predicting one dimensional power transfers a method which is based on space averaged quadratic variables and does not assume the restrictive assumptions of the statistical energy analysis sea such as high overlap or damping conditions is described the results are spatially more detailed than an sea response and of a lower computational cost than the one of the usual displacement formulation some of the quadratic variables used like energy densities or structural intensity retain a strong energy meaning even when time and space averaged their governing equation is derived for a homogeneous and isotropic medium with hysteretic damping the main originality of this work lies in considering complex structural intensity and establishing appropriate energetic boundary conditions for both active and reactive space averaged structural intensities by using the usual boundary conditions for the displacement field and the stress tensor the numerical examples prove that this space averaged quadratic method is well suited to describe global energy transfers along one dimensional dissipative structures in a frequency range for which the overlap is too low to obtain a quadratic response from the sea and solving the wave equation by using the finite element method fem would require more elements besides describing junctions with impedances makes the resonant behaviour of the system still accessible on frequency responses

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

complex envelope displacement analysis a quasi static approach to vibrations abstract a new model to analyze high frequency vibrations is presented instead of using the physical oscillating displacement the problem is described in terms of a complex envelope generated by an appropriate use of the hilbert transform the model can be put in the category of those methods that try to describe some representative characteristic of the oscillating solution average energy level thermal trend etc rather than the solution itself avoiding the computational problems connected with high frequency problems although the envelope solution by itself is sufficient and convenient to deal with structural acoustic coupling the proposed model presents the twofold advantage of avoiding computational problem connected with high frequency vibrations while keeping the capability of recovering the oscillating response when required

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

intrinsic characterization of space time symmetric tensors this paper essentially deals with the classification of a symmetric tensor on a four dimensional lorentzian space a method is given to find the algebraic type of such a tensor a system of concomitants of the tensor is constructed which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue and to obtain covariantly their eigenvectors some algebraic as well as differential applications are considered

numerical similarity and dissimilarity measures between two trees quantifying the measure of similarity between two trees is a problem of intrinsic importance in the study of algorithms and data structures and has applications in computational molecular biology structural syntactic pattern recognition and in data management in this paper we define and formulate an abstract measure of comparison spl omega t sub 1 t sub 2 between two trees t sub 1 and t sub 2 presented in terms of a set of elementary intersymbol measures spl omega and two abstract operators spl oplus and spl otimes by appropriately choosing the concrete values for these two operators and for spl omega this measure can be used to define various quantities including 1 the edit distance between two trees 2 the size of their largest common subtree 3 prob t sub 2 t sub 1 the probability of receiving t sub 2 given that t sub 1 was transmitted across a channel causing independent substitution and deletion errors and 4 the a posteriori probability of t sub 1 being the transmitted tree given that t sub 2 is the received tree containing independent substitution insertion and deletion errors the recursive properties of spl omega t sub 1 t sub 2 have been derived and a single generic iterative dynamic programming scheme to compute all the above quantities has been developed the time and space complexities of the algorithm have been analyzed and the implications of our results in both theoretical and applied fields has been discussed

algorithms for the constrained editing distance between ordered labeled trees and related problems abstract this paper considers the problem of computing a constrained editing distance between ordered labeled trees this distance metric can be applied to pattern recognition syntactic tree comparison classification tree comparison and other applications the problem of approximate ordered tree matching is also considered we present optimal algorithms for solving these problems in sequential time o t1 t2

generalized lcs the longest common subsequence lcs is a well studied problem having a wide range of implementations its motivation is in comparing strings it has long been of interest to devise a similar measure for comparing higher dimensional objects and more complex structures in this paper we study the longest common substructure of two matrices and show that this problem is np hard we also study the longest common subforest problem for multiple trees including a constrained version as well we show np hardness for k 2 unordered trees in the constrained lcs we also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees

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

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

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

homogeneous space times with seven isometries a new homogeneous space time with seven isometries is derived by means of a complex transformation it is shown that it is conformally flat and its weyl flat form is exhibited its killing vector fields and the corresponding lie algebra are also presented an integral representation of these vector fields is found sources for the new space time geometry are obtained by combining synge s approach to einstein s equations with energy conditions and segre classification of the energy momentum tensors a comparison with other rare space times possessing a g7 of motions is made by using a suite of computer algebra programs