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

experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

improving the efficiency of aerodynamic shape optimization the computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements the first improvement involves replacing a grid point based approach for surface representation with a bezier bernstein polynomial parameterization of the surface explicit analytical expressions for the grid sensitivity terms are developed for both approaches the second improvement proposes the use of newton s method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients

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

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

pseudo transient continuation for nonlinear transient elasticity this paper demonstrates how pseudo transient continuation improves the efficiency and robustness of a newton iteration within a non linear transient elasticity simulation pseudo transient continuation improves efficiency by enabling larger time steps than possible with a newton iteration robustness improves because pseudo transient continuation recovers the convergence of newton s method when the initial iterate is not within the region of local convergence we illustrate the benefits of pseudo transient continuation on a non linear transient simulation of a buckling cylinder including a comparison with a line search based newton iteration

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

aerodynamic design optimization using sensitivity analysis and computational fluid dynamics a new and efficient method is presented for aerodynamic design optimization which is based on a computational fluid dynamics cfd sensitivity analysis algorithm the method is applied to design a simplified scramjet afterbody configuration for an optimized axial thrust the euler equations are solved for the inviscid analysis of the flow which provides the objective function and the constraints of the optimization problem the cfd analysis is then coupled with the optimization procedure that used a constrained minimization method the sensitivity coefficients i e gradients of the objective function and the constraints needed for the optimization are obtained using a quasi analytic al method rather than the traditional finite difference approximations during the one dimensional search of the optimization procedure an approximate flow analysis predicted flow based on a first order taylor series expansion is used to reduce the computational cost finally the sensitivity of the optimum objective function to various flowfield problem parameters such as the mach number which are kept constant during the optimization is computed to predict new optimum solutions the flow analysis of the demonstrative example are compared with the experimental data it is shown that the method is more efficient than the traditional methods

pde constrained optimization with error estimation and control the paper describes an algorithm for pde constrained optimization that controls numerical errors using error estimates and grid adaptation during the optimization process a key aspect of the algorithm is the use of adjoint variables to estimate errors in the first order optimality conditions multilevel optimization is used to drive the optimality conditions and their estimated errors below a specified tolerance the error estimate requires two additional adjoint solutions but only at the beginning and end of each optimization cycle moreover the adjoint systems can be formed and solved with limited additional infrastructure beyond that found in typical pde constrained optimization algorithms the approach is general and can accommodate both reduced space and full space formulations of the optimization problem the algorithm is illustrated using the inverse design of a nozzle constrained by the quasi one dimensional euler equations

accurate aerodynamic sensitivity analysis using adjoint equations an accurate aerodynamic sensitivity analysis technique is described the current method uses the continuous adjoint approach to avoid excessive memory requirement and the dadi relaxation with multigrid acceleration for the fast convergence a derivation of the continuous adjoint operator is described for the 2nd order tvd scheme and a new anti diffusive flux is proposed for the adjoint equation to enhance the accuracy of sensitivity the accuracy of current method is demonstrated by solving sensitivity problem for 2 dimensional airfoils comparisons are also presented with finite difference results

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

cohomology of the space of polynomial maps on a1 with prescribed ramification abstract in this paper we study the moduli spaces simp n m of degree n 1 morphisms a k 1 a k 1 with ramification length simp n m is a zariski open subset of the space of degree n 1 polynomials over k up to a u t a k 1 it is in a way orthogonal to the many papers about polynomials with prescribed zeroes here we are prescribing instead the ramification data exploiting the topological properties of the poset that encodes the ramification behavior we use a sheaf theoretic argument to compute h simp n m c q as well as the etale cohomology h e t simp n m k q l for c h a r k 0 or c h a r k n 1 when n and m are such that n 3 m as a by product we obtain that h simp n m c q is independent of n thus implying rational cohomological stability when c h a r k 0 our methods compute h e t simp n m q l provided c h a r k n 1 and show that the etale cohomology groups in positive characteristics do not stabilize

the continuous adjoint method for the design of hydraulic turbomachines abstract this article presents the development and application of the continuous adjoint method for designing optimizing the shape of hydraulic turbomachines the reynolds averaged flow equations are solved in the rotating reference frame and the terms arising from the differentiation of the coriolis and centripetal forces are taken into account in the formulation of the adjoint equations the objective functions presented in this article can be used for achieving a the optimal collaboration of the runner impeller with the draft tube by controlling the meridional and circumferential velocity profiles at the exit of the runner b the operation at the desired hydraulic head and or c the cavitation suppression all of them are used to improve an existing francis runner it is important to note that the objective function related to cavitation is by definition non differentiable and a way to effectively handle it is proposed the continuous adjoint method is presented in its most general form and could readily be adapted to other objective functions in the field of hydraulic turbomachines

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

comparison of newton s and quasi newton s method solvers for the navier stokes equations the results of a computational evaluation of several newton s and quasi newton s method solvers are discussed and analyzed computer time and memory requirements for iterating a solution to the steady state are recorded for each method roe s flux difference splitting together with the spekreijse van albada continuous limiter is used for the spatial discretization sparse matrix inversions are performed using a modified version of the boeing real sparse library routines and the conjugate gradient squared algorithm the methods are applied to exact and approximate newton s method jacobian systems for flat plate and flat plate wedge type ge ometries results indicate that the quasi newton s method solvers do not exhibit quadratic convergence but can be more efficient than the exact newton s method in select cases consistent goal of computational fluid dynamics cfd research has been to improve the efficiency of numerical algorithms one measure of this efficiency is the log of the residual which varies linearly with iteration count for typical cfd techniques these methods can be expected to converge at the same rate no matter how close they are to the final solution an exception to this behavior is the quadratic convergence newton s method for which the convergence rate actually increases as the final solution is approached when quadratic convergence has been attained the number of cor rect digits in the solution doubles with each iteration this behavior has been illustrated by several researchers who have obtained solutions of the potential equation 1 the euler equa tions 2 5 and the navier stokes equations 2 4 6 13 unfortu nately the number of iterations is a less important measure of the efficiency of a code than the total computation time quadratic convergence rates are typically accompanied by significant increases in algorithm complexity and hence in creased per iteration computational requirements it was the intent of this research to explore how the conver gence rate and per iteration efficiency vary for similar new ton s and quasi newton s method solvers so that the most efficient computational strategy can be identified to accom plish this goal the quadratic convergence newton s method solver developed by orkwis and mcrae6 8 was modified to create several quasi newton s method solvers approxima tions were made to the form of the jacobian and to the jacobian matrix inversion process the resulting schemes are evaluated based on their robustness and efficiency for two test problems

variable fidelity aerodynamic optimization for turbulent flows using a discrete adjoint formulation an aerodynamic shape optimization methodology based on a discrete adjoint solver for navier stokes flows is described the flow solver at the heart of this optimization process is a reynolds averaged navier stokes code for multiblock structured grids it uses osher s approximate riemann solver and the algebraic turbulence model of baldwin lomax a corresponding discrete navier stokes adjoint solver is derived analytically it has to calculate accurately the jacobian including the effect of the turbulence modeling the shape deformations

newton krylov algorithm with a loosely coupled turbulence model for aerodynamic flows a fast newton krylov algorithm is presented that solves the turbulent navier stokes equations on unstructured 2 d grids the model of spalart and allmaras provides the turbulent viscosity and is loosely coupled to the mean flow equations it is often assumed that the turbulence model must be fully coupled to obtain the full benefit of an inexact newton algorithm we demonstrate that a loosely coupled algorithm is effective and has some advantages such as reduced storage requirements and smoother transient oscillations a transonic single element case converges to 1 1012 in 90 s on recent commodity hardware whereas the lift coefficient is converged to three figures in one quarter of that time

aerodynamic optimization algorithm with integrated geometry parameterization and mesh movement an efficient gradient based algorithm for aerodynamic shape optimization is presented the algorithm consists of several components including a novel integrated geometry parameterization and mesh movement a parallel newton krylov flow solver and an adjoint based gradient evaluation to integrate geometry parameterization and mesh movement generalized b spline volumes are used to parameterize both the surface and volume mesh the volume mesh of b spline control points mimics a coarse mesh a linear elasticity mesh movement algorithm is applied directly to this coarse mesh and the fine mesh is regenerated algebraically using this approach mesh movement time is reduced by two to three orders of magnitude relative to a node based movement the mesh adjoint system also becomes smaller and is thus amenable to complex step derivative approximations when solving the flow adjoint equations using restarted krylov subspace methods a nested subspace strategy is shown to be more robust than truncating the entire subspace optimization is accomplished using a sequential quadratic programming algorithm the effectiveness of the complete algorithm is demonstrated using a lift constrained induced drag minimization that involves large changes in geometry

direct and iterative algorithms for the three dimensional euler equations direct and iterative algorithms have been developed for solving a finite volume discretization of the three dimensional euler equations in curvilinear coordinates the euler equations are discretized using numerical derivatives of the numerical flux vector for the jacobians two direct solvers are formulated one of which has a diagonal plane matrix structure with significantly lower memory requirements the direct solvers are used as a benchmark in measuring the convergence rate and robustness of more computationally efficient solvers which include two factored approaches a newton relaxation algorithm and a discretized newton relaxation algorithm which uses numerical jacobians a diagonal plane formulation for the newton relaxation algorithms has also been developed that may have the potential for massive parallelization it is demonstrated that the newton relaxation approach can give convergence rates and robustness equal to that of a direct solver for three dimensional problems as a demonstration of the robustness of both the newton relaxation algorithm and numerical jacobians quadratic convergence to machine zero is demonstrated

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

newton s method solver for high speed viscous separated flowfields a new method for calculating the 2 d laminar navier stokes equations is presented the method uses newton s method for nonlinear systems of equations to find steady state solutions the navier stokes equations are approximated by finite differences using roe s flux difference splitting second order accuracy is attained by using spekreijse s interpolation with van albada s limiter the exact newton s method jacobian matrix is inverted by using recent sparse matrix routines the symbolic manipulation package macsyma is used to develop and write the fortran code

newton s method solver for the axisymmetric navier stokes equations a new two dimensional newton s method navier stokes solver is extended to the axisymmetric form of the equations roe s flux difference splitting is applied to the axisymmetric equations using glaister s approach a geometric conservation law correction term is added to insure satisfaction of the uniform stream reproduction criteria higher order accuracy is attained through the use of spekreijse s interpolation procedure with van albada s contiouous limiter harten and hyman s minimum eigenvalue correction is also included

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

three dimensional aerodynamic shape optimization using discrete sensitivity analysis an aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three dimensional geometries the function of sensitivity analysis is to directly couple computational fluid dynamics cfd with numerical optimization techniques which facilitates the construction of efficient direct design methods the development of a practical three dimensional design procedures entails many challenges such as 1 the demand for significant efficiency improvements over current design methods 2 a general and flexible three dimensional surface representation and 3 the efficient solution of very large systems of linear algebraic equations it is demonstrated that each of these challenges is overcome by 1 employing fully implicit newton methods for the cfd analyses 2 adopting a bezier bernstein polynomial parameterization of two and three dimensional surfaces and 3 using preconditioned conjugate gradient like linear system solvers whereas each of these extensions independently yields an improvement in computational efficiency the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use the new aerodynamic shape optimization procedure is demonstrated in the design of both two and three dimensional inviscid aerodynamic problems including a two dimensional supersonic internal external nozzle two dimensional transonic airfoils resulting in supercritical shapes three dimensional transport wings and three dimensional supersonic delta wings each design application results in realistic and useful optimized shapes

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

studies of numerical methods for the plane navier stokes equations abstract in the present report and in our most recent work we have concentrated on three basic formulations primitive variables vorticity stream function and stream function biharmonic formulation with each such formulation there are a variety of difference equations that could be used and then there are a large number of iteration schemes that could be employed to solve these difference equations the ultimate goal of course is to find the best combination of all these techniques

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

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

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

new approach to constrained shape optimization using genetic algorithms a robust genetic algorithm for constrained functional optimization is described the function being sought is represented both in a piecewise linear fashion and in two different types of orthogonal series representations satisfying in each case specified end conditions of both dirichlet and neumann types the search for the optimal function is translated to one of determining the coefficients of a series expansion and a genetic algorithm is developed for this purpose the method is validated in terms of test problems for which the global optimum solutions are known the results indicate that if the population size of the chromosome pool is held constant the performance of the piecewise linear representation approach deteriorates considerably as the number of degrees of freedom increases in contrast the orthogonal series representations do not suffer from this drawback and a significant reduction in the population size can be achieved therefore the latter methodology offers a far more efficient approach to functional optimization than previously attempted the developed methodology was applied to the determination of an optimal micropump shape the genetic algorithm uncovered shapes that were nonintuitive but yielded vastly superior pump performance

computing the similarity of two sequences with nested arc annotations we present exact algorithms for the np complete longest common subsequence problem for sequences with nested arc annotations a problem occurring in structure comparison of rna given two sequences of length at most n and nested arc structure one of our algorithms determines if existent in o 3 31k1 k2 n time an arc preserving subsequence of both sequences which can be obtained by deleting together with corresponding arcs k1 letters from the first and k2 letters from the second sequence a second algorithm shows that in case of a four letter alphabet we can find a length l arc annotated subsequence in o 12l l n time this means that the problem is fixed parameter tractable when parameterized by the number of deletions as well as when parameterized by the subsequence length our findings complement known approximation results which give a quadratic time factor 2 approximation for the general and polynomial time approximation schemes for restricted versions of the problem in addition we obtain further fixed parameter tractability results for these restricted versions

drag minimization based on the navier stokes equations using a newton krylov approach a methodology is presented for performing numerical aerodynamic shape optimization based on the three dimensional reynolds averaged navier stokes rans equations an initial multiblock structured mesh is first fit with b spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on b spline surfaces the rans equations and the one equation spalart allmaras turbulence model are solved in a fully coupled manner using an efficient parallel newton krylov algorithm with approximate schur preconditioning gradient evaluations are performed using the discrete adjoint approach with analytical differentiation of the discrete flow and mesh movement equations the overall methodology remains robust even in the presence of large shape changes several examples of lift constrained drag minimization are provided including a study of the common research model wing geometry a wing body tail geometry with a prescribed spanwise load distributi

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

driven cavity flows by efficient numerical techniques abstract efficient and reliable numerical techniques of high order accuracy are presented for solving problems of steady viscous incompressible flow in the plane and are used to obtain accurate solutions for the driven cavity a solution is obtained at reynolds number 10 000 on a 180 180 grid the numerical methods combine an efficient linear system solver an adaptive newton like method for nonlinear systems and a continuation procedure for following a branch of solutions over a range of reynolds numbers

stability analysis and aerodynamic design optimization of euler equations using variational methods the one and two dimensional inviscid euler equations are formulated in an integro differential form for shape design sensitivity analysis and optimization the principal tool employed to derive the performance derivative sensitivity equations is the variational method which is a continuous alternative to the discrete sensitivity analysis along with the sensitivity equations the co state equations and their boundary conditions are derived thereafter based on the modal analysis of von neumann theory the stability limits of the co state equations are investigated the stability characteristics of the co state equations are compared with those of the euler equations finally using the criteria from the stability analysis of the state and co state equations some results of shape design optimization and sensitivity analysis for both quasi one and two dimensional euler equations are presented copyright 1999 john wiley sons ltd

cfd shape optimization using an incomplete gradient adjoint formulation a design methodology based on the adjoint approach for flow problems governed by the incompressible euler equations is presented the main feature of the algorithm is that it avoids solving the adjoint equations which saves an important amount of cpu time furthermore the methodology is general in the sense it does not depend on the geometry representation all the grid points on the surface to be optimized can be chosen as design parameters in addition the methodology can be applied to any type of mesh the partial derivatives of the flow equations with respect to the design parameters are computed by finite differences in this way this computation is independent of the numerical scheme employed to obtain the flow solution once the design parameters have been updated the new solid surface is obtained with a pseudo shell approach in such a way that local singularities which can degrade or inhibit the convergence to the optimal solution are avoided some 2d and 3d numerical examples are shown to demonstrate the proposed methodology copyright 2001 john wiley sons ltd

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

using an adjoint approach to eliminate mesh sensitivities in computational design an adjoint algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced the method eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables an expense that has hindered large scale design optimization for practical applications the effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation followed by an explicit matrix vector product whose cost scales with the number of design variables and the resolution of the parameterized surface grid the methodology augments the current practice of using adjoints solely for the flowfield and leads to a dramatic computational savings the accuracy of the implementation is established and several sample design optimizations are shown

efficient aerodynamic design method using a tightly coupled algorithm an efe cient aerodynamic design optimization method for the compressible euler equations is presented a gradient based optimization method is used to e nd the optimal design in conjunction with a continuous adjoint sensitivity analysis method to improve the efe ciency of the design method a tightly coupled algorithm based on a step size estimation isproposed the efe ciency of thepresentmethod is demonstrated through drag minimizations of a wing and an airfoil the result shows that the cost of the present method is signie cantly lower than that of the loosely coupled algorithm nomenclature ci e ux jacobian matrix in the computational domain d design variables vector fi e ux vector in the computational domain fi e ux vector in the physical domain g gradient vector of the object function i object function q conservative e ow variables vector r residual vector in the computational domain s searching direction step size along the searching direction s a lagrangian multiplier vector subscript face value at cell face superscript t transpose of vector or matrix

mesh movement for a discrete adjoint newton krylov algorithm for aerodynamic optimization a grid movement algorithm based on the linear elasticity method with multiple increments is presented the methodisrelativelycomputationallyexpensivebutisexceptionallyrobust producinghigh qualityelementsevenfor large shape changes it is integrated with an aerodynamic shape optimization algorithm that uses an augmented adjoint approach for gradient calculation the discrete adjoint equations are augmented to explicitly include the sensitivities of the mesh movement resulting in an increase in efficiency and numerical accuracy this gradient computation method requires less computational time than a function evaluation and leads to significant computational savings as dimensionality is increased the results of the application of these techniques to several large deformation and optimization cases are presented

continuous adjoint sensitivities for optimization with general cost functionals on unstructured meshes a continuous adjoint approach is developed to obtain the sensitivity derivatives for the euler equations the completederivationofthecostateequations andtheirtransversality boundary conditionsarepresented both the state and the costate equations are second order e nite volume discretized for unstructured meshes and they are coupled with a constrained optimization algorithm also integrated into the overall methodology are a geometry parameterization method for the shape optimization and a dynamic unstructured mesh method for the shape evolution and the consequent volume mesh adaptations for the proof of concept three transonic airfoil optimization problems are presented this method accepts general cost functionals which are not necessarily functions of pressure only it is also shown that a switch to the natural coordinate system in conjunction with the reduction of the governing state equation to the control surface results in sensitivity integrals that are only a function of the tangential derivativesof the state variables thisapproach eliminates the need fornormal derivativecomputations that can be erroneous

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

homological stability for hurwitz spaces and the cohen lenstra conjecture over function fields we prove a homological stabilization theorem for hurwitz spaces moduli spaces of branched covers of the complex projective line this has the following arithmetic consequence let 2 be prime and a a nite abelian group then there exists q q a such that for q greater than q a positive fraction of quadratic extensions of fq t have the part of their class group isomorphic to a

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

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

comparison of numerical and analytical jacobians the results are presented of comparison between numerical and analytical approaches for forming the jacobian matrices that arise from implicit discretizations of the governing equations the derivation of the exact analytical jacobians using the macsyma symbolic manipulation expert system is discussed in detail the numerical differentiation procedure used to develop the numerical jacobians is described the jacobian entries obtained from the preceding approaches were tested by comparing the density residuals obtained for selected test cases the test cases include supersonic flat plate and compression corner geometries the results indicate that the two approaches are virtually identical although the numerical jacobian approach may have some implementation advantages over the exact analytical approach

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

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

aerodynamic shape optimization using preconditioned conjugate gradient methods in an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure it is demonstrated that preconditioned conjugate gradient like methodologies dramatically decrease the computational efforts required for such procedures the design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric naca 0012 airfoil in inviscid transonic flow and at zero degrees angle of attack the complete surface shape is represented using a bezier bernstein polynomial

nonconsistent mesh movement and sensitivity calculation on adjoint aerodynamic optimization this paper presents an investigation of the influence of a nonconsistent approach in terms of mesh movement and mesh sensitivity calculation in a discrete adjoint based optimization some mesh movement methods are more robust or of higher quality whereas others can be more efficient for calculating mesh sensitivity it is found that a nonconsistent approach gives comparable results when compared to a consistent approach therefore an appropriate combination of nonconsistent approaches can be achieved for efficient adjoint optimization this paper investigates and compares various consistent and nonconsistent combinations by using linear elasticity delaunay graph mapping and radial basis function mesh movement methods an investigation is presented using a lift constrained drag minimization to assess which step of the chain introduces a deviation if any and to which degree this affects the final result

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

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

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

numerical methods in markov chain modeling this paper describes and compares several methods for computing stationary probability distributions of markov chains the main linear algebra problem consists of computing an eigenvector of a sparse nonsymmetric matrix associated with a known eigenvalue it can also be cast as a problem of solving a homogeneous singular linear system we present several methods based on combinations of krylov subspace techniques single vector power iteration relaxation procedures and acceleration techniques we compare the performance of these methods on some realistic problems

infeasible path optimal design methods with applications to aerodynamic shape optimization we consider optimal design of physical systems described by a nonlinear boundary value problem we propose a sequential quadratic programming method specifically tailored to the solution of this class of design problems a particular representation of the null space of the constraint jacobian that exploits its specific structure is employed the resulting method avoids resolution of nonlinear behavior at the optimization iterations while keeping the size of the problem as small as that of conventional approaches three variants of the method are developed and discussed these entail the solution of either two or three linear systems involving the jacobian matrix of the discretized form of the boundary value problem the method is used to solve aerodynamic design problems involving nonlinear transonic flow no special provisions are made for treating discontinuities and therefore the present implementation of the method is limited to problems with no shocks problems with up to 90 shape design variables are solved numerical results demonstrate a substantial performance improvement over conventional methods

optimized nonuniform rational b spline geometrical representation for aerodynamic design of wings the geometric representation and parameterization used in an aerodynamic wing design process determines the number of design variables and influences the smoothness of the wing representation in an attempt to reduce the number of design variables while preserving good smoothness properties the present research investigates the performance of an optimized nonuniform rational b spline nurbs geometrical representation for the aerodynamic design of wings as a first step an approach is described whereby optimal spatial positions and weights of a fixed number of nurbs control points is determined using a quasi newton optimization algorithm to approximate a general airfoil section the resulting optimized nurbs representation significantly reduces the number of design variables needed to define accurately a wing section while ensuring good smoothness properties in a second step the nurbs control point positions and weights are used as design variables in an aerodynamic optimization problem this methodology results in a rapid and robust design process as illustrated by examples of aerodynamic optimization for two and three dimensional cases

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

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

difficulties in sensitivity calculations for flows with discontinuities the use of flow sensitivities has become an integral part of flow optimization based aerodynamic design and is useful for the efficient calculation of perturbed flows however there are still many issues to be resolved especially for flows having discontinuities flow sensitivities for several numerical methods are calculated using finite difference quotients automatic differentiation and the sensitivity equation method the flow sensitivities are calculated for the riemann problem of gas dynamics an attempt is made to expose explain and understand difficulties that arise in the calculation of flow sensitivities in flows with discontinuities

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

an approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives in this study involving advanced fluid flow codes an incremental iterative formulation also known as the delta or correction form together with the well known spatially split approximate factorization algorithm is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis for smaller 2d problems a direct method can be applied to solve these linear equations in either the standard or the incremental form in which case the two are equivalent iterative methods are needed for larger 2d and future 3d applications however because direct methods require much more computer memory than is currently available iterative methods for solving these equations in the standard form are generally unsatisfactory due to a lack of diagonal dominance and perhaps ill conditioning of the coefficient matrix this problem can be overcome when these equations are cast in the incremental form these and other benefits are discussed herein the methodology is successfully implemented and tested in 2d using an upwind cell centered finite volume formulation applied to the thin layer navier stokes equations results are presented for two sample airfoil problems 1 subsonic low reynolds number laminar flow and 2 transonic high reynolds number turbulent flow

sensitivity derivatives for three dimensional supersonic euler code using incremental iterative strategy in a recent work an incremental strategy was proposed to iteratively solve the very large systems of linear equations that are required to obtain quasianalytical sensitivity derivatives from advanced computational fluid dynamics cfd codes the technique was sucessfully demonstrated for two large two dimensional problems a subsonic and a transonic airfoil the principal feature of this incremental iterative stategy is that it allows the use of the identical approximate coefficient matrix operator and algorithm to solve the nonlinear flow and the linear sensitivity equations at convergence the accuracy of the sensitivity derivatives is not compromised this feature allows a comparatively straightforward extension of the methodology to three dimensional problems this extension is successfully demonstrated in the present study for a space marching solution of the three dimensional euler equations over a mach 2 4 blended wing body configuration

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

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

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

numerical and theoretical considerations for sensitivity calculation of discontinuous flow abstract linearization of 1 d euler equations about a discontinuous solution is discussed from both the theoretical and numerical point of view estimates for the norm of the solution of the linearized system are shown to be valid for the case presented numerically the linearization is performed following the guidelines of tangent linear model and sensitivities with respect to a flow parameter are computed being in better agreement with the analytical value when compared with previously reported numerical results

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

efficient pattern matching for rna secondary structures we propose efficient methods to address key pattern matching problems in rna secondary structures using the notion of structural strings a structural string s string is composed of constant symbols and parameter symbols from the alphabets and respectively an individual symbol in the alphabet may be considered a complement of another unique symbol in the notion of matching constants parameters and complements is referred to as the structural matching s match problem which is helpful in matching rna and previously was solved by the structural suffix tree sst other approaches to rna matching that do not openly consider the s match include the use of affix data structures in this paper we provide new data structures and algorithms to address the s match problem specifically we introduce the structural suffix array and structural longest common prefix array and then identify how to s match with these data structures our new s matching solution is then used as the framework to answer various combinatorial queries encountered in matching rna secondary structures

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 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