weighted estimates for the helmholtz equation and some applications we characterize the radial functionsvin rnfor which the a priori inequality u1 2 2 k uv1 2 2 c v 1 2 k2 u 2holds with constant independent ofk the condition is forvto have the x rays transform everywhere bounded we apply these estimates to the well posedness of evolution schrodinger equations with time dependent drift terms and to the restriction of the fourier transform to euclidean spheres

global regularity for the maxwell klein gordon equation with small critical sobolev norm in high dimensions we show that in dimensions n 6 one has global regularity for the maxwell klein gordon equations in the coulomb gauge provided that the critical sobolev norm open image in new window of the initial data is sufficiently small these results are analogous to those recently obtained for the high dimensional wave map equation 17 7 14 12 but unlike the wave map equation the coulomb gauge non linearity cannot be iterated away directly we shall use a different approach proving strichartz estimates for the covariant wave equation this in turn will be achieved by use of littlewood paley multipliers and a global parametrix for the covariant wave equation constructed using a truncated microlocalized cronstrom gauge

a decomposition theorem and two algorithms for reticulation visible networks in studies of molecular evolution phylogenetic trees are rooted binary trees whereas phylogenetic networks are rooted acyclic digraphs edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks for the purpose of validating evolutionary models biologists check whether or not a phylogenetic tree resp cluster is contained in a phylogenetic network on the same taxa these tree and cluster containment problems are known to be np complete a phylogenetic network is reticulation visible if every reticulation node separates the root of the network from at least a leaf we answer an open problem by proving that the tree containment problem is solvable in quadratic time for reticulation visible networks the key tool used in our answer is a powerful decomposition theorem it also allows us to design a linear time algorithm for the cluster containment problem for networks of this type and to prove that every galled network with n leaves has 2 n 1 reticulation nodes at most

on finding the rectangular duals of planar triangular graphs this paper presents a new linear time algorithm for finding rectangular duals of planar triangular graphs the algorithm is conceptually simpler than the previously known algorithm the coordinates of the rectangular dual constructed by the new algorithm are integers and carry clear combinatorial meaning

generalized substring compression in substring compression one is given a text to preprocess so that upon request a compressed substring is returned generalized substring compression is the same with the following twist the queries contain an additional context substring or a collection of context substrings and the answers are the substring in compressed format where the context substring is used to make the compression more efficient we focus our attention on generalized substring compression and present the first non trivial correct algorithm for this problem inherent to our algorithm is a new method for finding the bounded longest common prefix of substrings which may be of independent interest in addition we propose an efficient algorithm for substring compression which makes use of range successor queries we present several tradeoffs for both problems for compressing the substring s i j possibly with the substring s email protected as a context the best query times we achieve are o c and o clog j ic for substring compression query and generalized substring compression query respectively where c is the number of phrases encoded a preliminary version of this paper has been presented in 21

coupling of two and three dimensional composite shell elements in linear and non linear applications abstract a numerical model for the non linear analysis of laminates is presented the developed element is based on piecewise polynomial interpolation in thickness direction although the total number of degrees of freedom is comparable to a discretization with 3d brick elements this approach provides several advantages e g a simple mesh generation due to a 2d type data structure and a better bending behavior the developed isoparametric quadrilateral finite element allows prediction of the complete stress state furthermore a transition element is presented which is used to couple the developed element with 5 parameter shell elements several linear and non linear examples are presented to illustrate the performance of the developed numerical model

updated lagrangian formulation of a flat triangular element for thin laminated shells an updated lagrangian formulation of a three node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells the flat shell element is obtained by combining the discrete kirchhoff theory plate bending element and a membrane element that is similar to the allman element but a derivative of the linear strain triangular element results are presented for large rotation static response analysis of a cantilever beam under end moment cylindrical shell under pinching and stretching loads a hemispherical shell under pinching and stretching loads and a ring plate under a line load for dynamic response analysis of a cylindrical panel and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel to estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures static analysis of an apex loaded circular arch is performed the arch is a building block of a large inflatable structure the results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software abaqus demonstrating the accuracy of the present formulation he two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly the curved shell elements can be computationally very expensive especially in the case of nonlinear analysis because of the complexity of the formulation and the need to compute the curvature information flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements though a large number of elements are required to accurately model curved structures the analysis is computational ly less expensive because of extremely simple formulation updated lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature in an updated lagrangian formulation all of the variables are referred to a known configuration the reference configuration which is updated continuously during the deformation process if the rigid body modes are removed from the total or incremental displacements the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used in a linearized incremental formulation the stresses are computed using linear strain displacement relations the tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix the stiffness matrices resulting from the nonlinear terms in the strain displacement relations are neglected resulting in very economical analysis if the rigid body modes are not removed all nonlinear terms in the strain displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix a three node flat triangular shell element was introduced by argyris et al 2 for nonlinear elastic stability problems this formula

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

nonlinear free vibrations of composite plates abstract the evolution of the natural mode method nmm for finite element analysis of complex composite structures continues in the present study by applying its principles and formulating the kinematically consistent matrix of a model three node multilayered triangular element both translational and rotational inertia are included in the mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element linear eigenfrequencies are validated with experimental and finite element solutions subsequently the large amplitude nonlinear undamped free vibration of composite plates is investigated a computational scheme is conceived whereby the structure is initially displaced by conducting a full geometrically nonlinear static analysis and subsequently set to transient nonlinear free oscillations by removing the static loading in this regard we discuss the two structured eulerian convective computational schemes employed namely the ariban scheme accumulation of rigid body and natural modes for static nonlinear analysis and the cubic hermitian scheme cuherm for large displacement transient deformation numerical examples demonstrate the efficiency of the formulation and the potential of the natural mode method to deal vigorously with intricate nonlinear time dependent phenomena as well as its potential to provide answers for larger and more complex structures the study also indicates the efficiency and tailoring flexibility offered by advanced composite structural systems

bounded hairpin completion hairpin completion is a formal operation inspired from biochemistry here we consider a restricted variant of hairpin completion called bounded hairpin completion applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x hairpin completion produces a new word z which is a prolongation of x to the right or to the left by annealing although this operation is a purely mathematical one and the biological reality is just a source of inspiration it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion the restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion they cannot be longer than a given constant closure properties of some classes of formal languages under the non iterated and iterated bounded hairpin completion are investigated we consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them finally also the inverse operation namely bounded hairpin reduction as well as the set of all primitive bounded hairpin roots of a regular language are considered

from gene trees to species trees this paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model this is a fundamental problem in computational molecular biology our main results are as follows a linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree this answers a problem raised recently by eulenstein mirkin and vingron j comput bio 5 1998 pp 135 148 the complexity of finding an optimal species tree from gene trees is studied the problem is proved to be np hard for the duplication cost and for the mutation cost further the concept of reconciled trees was introduced by goodman et al and formalized by page for visualizing the relationship between gene and species trees we show that constructing an optimal reconciled tree for gene trees is also np hard finally we consider a general reconstruction problem and show it to be np hard even for the well known nearest neighbor interchange distance a new and efficiently computable metric is defined based on the duplication cost we show that the problem of finding an optimal species tree from gene trees is np hard under this new metric but it can be approximated within factor 2 in polynomial time using this approximation result we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other our heuristic method is significantly better than the existing program in page s genetree 1 0 that starts the search from a random tree

area universal and constrained rectangular layouts a rectangular layout is a partition of a rectangle into a finite set of interior disjoint rectangles these layouts are used as rectangular cartograms in cartography as floorplans in building architecture and vlsi design and as graph drawings often areas are associated with the rectangles of a rectangular layout and it is desirable for one rectangular layout to represent several area assignments a layout is area universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout we identify a simple necessary and sufficient condition for a rectangular layout to be area universal a rectangular layout is area universal if and only if it is one sided we also investigate similar questions for perimeter assignments the adjacency requirements for the rectangles of a rectangular layout can be specified in various ways most commonly via the dual graph of the layout we show how to find an area universal layout for a given set of adjacency requirements whe

nonlinear dynamic analysis of shells with the triangular element tric abstract tric is a facet triangular shell element which is based on the natural mode method it has been shown that the tric shell element satisfies the individual element test and in the framework of the nonconsistent formulation the convergence requirements are fulfilled while it has been proved to be very efficient in linear and nonlinear static problems moreover another major advantage in the formulation of this element is the incorporation of the transverse shear deformations in a way that defies the shear locking phenomenon in this work the derivation of the consistent and lumped mass matrices of the tric element is presented so that it can be used in linear and nonlinear dynamic problems both translational and rotational inertia are included in the consistent mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element all the kinematical and geometrical arguments that are invoked for the derivation of the consistent mass matrix are briefly presented moreover two formulations of the lumped mass matrix of tric are derived the first formulation is based entirely on geometrical considerations whereas the second is based on lumping the consistent mass matrix of tric finally the element s robustness and accuracy will be shown by applying it to properly selected benchmark examples of nonlinear shell dynamics while its computational efficiency will be demonstrated by comparing the cpu performance of the element with the other available shell elements

common face embeddings of planar graphs given a planar graph ggg and a sequence cc 1 ldots cc q where each cc i is a family of vertex subsets of ggg we wish to find a plane embedding of ggg if any exists such that for each i in 1 ldots q there is a face fi in the embedding whose boundary contains at least one vertex from each set in cci this problem has applications in the recovery of topological information from geographical data and the design of constrained layouts in vlsi let inputsize be the input size i e the total number of vertices and edges in ggg and the families cci counting multiplicity we show that this problem is np complete in general we also show that it is solvable in o inputsize log inputsize time for the special case in which for each input family cci each set in cci induces a connected subgraph of the input graph ggg note that the classical problem of simply finding a planar embedding is a further special case of this case with q 0 therefore the processing of the additional constraints cc1 ccq incurs only a logarithmic factor of overhead

dynamic 3 sided planar range queries with expected doubly logarithmic time the priority search tree is the classic solution for the problem of dynamic 2 dimensional searching for the orthogonal query range of the form a b x c 3 sided rectangle it supports all operations in logarithmic worst case complexity in both main and external memory in this work we show that the update and query complexities can be improved to expected doubly logarithmic when the input coordinates are being continuously drawn from specific probability distributions we present three pairs of linear space solutions for the problem i e a ram and a corresponding i o model variant 1 first we improve the update complexity to doubly logarithmic expected with high probability under the most general assumption that both the x and y coordinates of the input points are continuously being drawn from a distribution whose density function is unknown but fixed 2 next we improve both the query complexity to doubly logarithmic expected with high probability and the update complexity to doubly logarithmic amortized expected by assuming that only the x coordinates are being drawn from a class of smooth distributions and that the deleted points are selected uniformly at random among the currently stored points in fact the y coordinates are allowed to be arbitrarily distributed 3 finally we improve both the query and the update complexity to doubly logarithmic expected with high probability by moreover assuming the y coordinates to be continuously drawn from a more restricted class of realistic distributions all data structures are deterministic and their complexity s expectation is with respect to the assumed distributions they comprise combinations of known data structures and of two new data structures introduced here namely the weight balanced exponential tree and the external modified priority search tree

thermomechanical response of solids at high strains natural approach abstract the paper develops in pursuance of 4 the theoretical framework appertaining to coupled thermomechanical deformations of solids subject to large as well as inelastic deformations the essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects on the other hand it must be admitted that current concepts on mechanical constitutive assumptions 5 6 are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account furthermore algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and in particular quasi newton techniques are discussed the paper concludes with a number of applications of technical relevance

on the construction of classes of suffix trees for square matrices we provide a uniform framework for the study of index data structures for a two dimensional matrixtext1 n 1 n whose entries are drawn from an ordered alphabet an index fortextcan be informally seen as the two dimensional analog of the suffix tree for a string it allows on line searches and statistics to be performed ontextby representing compactly the n3 square submatrices oftextin optimalo n2 space we identify 4n 1families of indices fortext each containing ni 1 2i 1 isomorphic data structures we also develop techniques leading to a single algorithm that efficiently builds any index in any family ino n2logn time ando n2 space such an algorithm improves in various respects the algorithms for the construction of the pat tree and the lsuffix tree the framework and the algorithm easily generalize tod 2 dimensions moreover as part of our algorithm we provide new algorithmic tools that yield a space efficient implementation of the naming scheme of r karpet al in proceedings fourth symposium on theory of computing pp 125 136 for strings and matrices

good spanning trees in graph drawing introduces a good spanning tree of a plane graph solves two open problems on monotone drawings using good spanning trees finds a 2 visibility drawing of a planar graph using a good spanning tree gives algorithms to find an spike vpg and t shaped drawings of a planar graph a plane graph is a planar graph with a fixed planar embedding in this paper we define a special spanning tree of a plane graph which we call a good spanning tree not every plane graph has a good spanning tree we show that every connected planar graph has a planar embedding with a good spanning tree using a good spanning tree we show that every connected planar graph g of n vertices has a straight line monotone grid drawing on an o n o n 2 grid and such a drawing can be found in o n time our results solve two open problems on monotone drawings of planar graphs posed by angelini et al using good spanning trees we also give simple linear time algorithms for finding a 2 visibility representation of a connected planar graph g of n vertices on a 2 n 1 2 n 1 grid and for finding a spike vpg representation of g on a 2 n 1 n grid

improved data structures for fully dynamic biconnectivity we present fully dynamic algorithms for maintaining the biconnected components in general and plane graphs a fully dynamic algorithm maintains a graph during a sequence of insertions and deletions of edges or isolated vertices let m be the number of edges and n be the number of vertices in a graph the time per operation of the best deterministic algorithms is o sqrt n in general graphs and o log n in plane graphs for fully dynamic connectivity and o min m2 3 n in general graphs and o sqrt n in plane graphs for fully dynamic biconnectivity we improve the later running times to o sqrt m log n in general graphs and o log 2 n in plane graphs our algorithm for general graphs can also find the biconnected components of all vertices in time o n

self adjusting binary search trees the splay tree a self adjusting form of binary search tree is developed and analyzed the binary search tree is a data structure for representing tables and lists so that accessing inserting and deleting items is easy on an n node splay tree all the standard search tree operations have an amortized time bound of o log n per operation where by amortized time is meant the time per operation averaged over a worst case sequence of operations thus splay trees are as efficient as balanced trees when total running time is the measure of interest in addition for sufficiently long access sequences splay trees are as efficient to within a constant factor as static optimum search trees the efficiency of splay trees comes not from an explicit structural constraint as with balanced trees but from applying a simple restructuring heuristic called splaying whenever the tree is accessed extensions of splaying give simplified forms of two other data structures lexicographic or multidimensional search trees and link cut trees

regular edge labeling of 4 connected plane graphs and its applications in graph drawing problems abstract in this paper we extend the concept of the regular edge labeling for general plane graphs and for triconnected triangulated plane graphs to 4 connected triangulated plane graphs we present two different linear time algorithms for constructing such a labeling by using regular edge labeling we present a new linear time algorithm for constructing rectangular dual of planar graphs our algorithm is simpler than previously known algorithms the coordinates of the rectangular dual constructed by our algorithm are integers while the one constructed by known algorithms are real numbers our second regular edge labeling algorithm is based on canonical ordering of 4 connected triangulated plane graphs by using this technique we present a new algorithm for constructing visibility representation of 4 connected planar graphs our algorithm reduces the size of the representation by a factor of 2 for such graphs

novel transformation techniques using q heaps with applications to computational geometry using the notions of q heaps and fusion trees developed by fredman and willard we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces in particular we develop a fast fractional cascading technique which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by o log epsilon n for some constant epsilon 0 where n is the total size of all the lists stored in the tree we apply the fast fractional cascading technique in combination with the other techniques to derive the first linear space sublogarithmic time algorithms for two fundamental geometric retrieval problems orthogonal segment intersection and rectangular point enclosure

semi analytical finite elements in the higher order theory of beams abstract the paper presents semi analytical finite elements leading to the development of a higher order theory for beams an analysis of existing beam theories reveals their semi analytical character the semi analytical finite element sfe method proposed assumes the cross section of a solid beam to be an assemblage of certain semi analytical elements the sfe method is based on independent approximations of three dimensional fields of displacements and stresses the method reflects the multi level nature of beams where conventional finite elements are transferred to the level of beam equations for heuristic considerations a mathematical formulation of the linear theory of a solid beam involves the equations of compatibility equilibrium and constitutive relationships i e the elastic law as well as static and kinematic boundary conditions compatibility conditions are derived directly by using finite element approximations while equilibrium equations constitutive equations and boundary conditions may be derived by applying stationarity of a modified hellinger reissner functional this derivation may be also defined by straightforward application of a generalised virtual work formulation the equations of a beam are formulated in terms of generalised variables integral resultants of stresses and strains as well as of nodal displacements the definition of generalised variables is assigned to the nodes of the finite element mesh bending warping and other higher order deformation modes are described automatically finally the set of governing equations includes mixed algebraic differential operators their explicit expressions depend on one of the element types isoparametric subparametric or superparametric the versatility of sfe is demonstrated in practical applications involving well known solutions the classical euler bernoulli and timoshenko theories are derived using a single one dimensional element the beams with a thin walled cross section are described as an assemblage of semi analytical elements on the basis of a higher order theory the conventional semi analytically based finite elements sabfe are derived their basic relations are also presented some numerical examples of the applications to thin walled beams illustrate the basic features possible extensions of sfe to dynamics geometric non linearity and shells are briefly discussed

on the complexity of covering vertices by faces in a planar graph the pair g d consisting of a planar graph g v e with n vertices together with a subset of d special vertices d subseteq v is called k planar if there is an embedding of g in the plane so that at most k faces of g are required to cover all of the vertices in d checking 1 planarity can be done in linear time since it reduces to a problem of checking planarity of a related graph we present an algorithm which given a graph g and a value k either determines that g is not k planar or generates an appropriate embedding and associated minimum cover in o c k n time where c is a constant hence the algorithm runs in linear time for any fixed k the fact that the time required by the algorithm grows exponentially in k is to be expected since we also show that for arbitrary k the associated decision problem is strongly np complete even when the planar graph has essentially a unique planar embedding d theta n and all facial cycles have bounded length these results provide a polynomial t

endpoint estimates for commutators of singular integral operators abstract we prove endpoint estimates for commutatotrs of singular integrals with bmo functions we first show that they satisfy l log l type inequalities and then that there is a hardy space type estimate where the usual atomic hardy space is replaced by an appropriate subspace

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

a multilayer composite triangular element for steady state conduction convection radiation heat transfer in complex shells abstract our latest study presents the theoretical formulation and computer implementation of a three node six degrees of freedom multilayer flat triangular element intended for the study of the temperature fields in complex multilayer composite shells inherent in the formulation in this first introductory and self consistent systematic study are the three modes of heat transfer namely conduction convection and radiation the latter introducing in our theoretical model strong nonlinear effects in the present discourse all nonlinear terms are strictly due to radiation the material properties are assumed independent of temperature but this in no way restricts the generality of the basic theory the formulation is based on a first order thermal lamination theory which assumes a linear through the thickness temperature variation the following features are uniquely implemented in the computer model 1 1 exact integration of all matrices including the highly nonlinear radiation matrix 2 2 exact integration of all derivative jacobian matrices for efficient nonlinear analysis 3 3 geometrical generality achieved by an arbitrarily oriented inexpensive flat shell element 4 4 compatibility with structural elements 5 5 computational efficiency and simplicity a predictor corrector scheme in the form of the newton raphson method is adopted for the solution of the stead state nonlinear problem numerical examples ranging from simple panels to complex anisotropic shells substantiate the theoretical formulation and show the potential of the present laminated triangular element in the computer simulation of temperature effects in complex geometries

on a calderon zygmund commutator type estimate abstract in this paper we present a calderon zygmund commutator type estimate this estimate enables us to prove an embedding result concerning weighted function spaces

explanation and elimination of shear locking and membrane locking with field consistence approach abstract in this paper in the context of beam elements shear locking and membrane locking are explained and cured in a unified way with a field consistence approach in the view of field consistence approach when transverse displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are adopted shear locking will occur similarly when in plane displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are used membrane locking will happen the beam elements derived by field consistence approach are not only free of shear locking and membrane locking but also highly efficient compared with their isoparametric counterparts although theoretically the internal forces generalized strains in mixed variational principles can vary independently they are neither independent to each other nor independent of displacement fields from the point of view of the field consistence approach

optimal parallel 5 colouring of planar graphs we show that a 5 colouring of the vertices of an n vertex planar graph may be computed in o log n log n time by an exclusive read exclusive write parallel ram with o n log n log n processors our algorithm while faster than all previously known methods is at the same time the first parallel 5 colouring algorithm to exhibit an optimal speedup optimality is achieved through a method based on the accelerating cascades technique and of independent interest it should be emphasized that although input to the algorithm is a planar graph we do not require a planar embedding to be given as part of the input other results concern the colouring of graphs of bounded genus and the construction of search structures for triangular planar subdivisions

arboricity and subgraph listing algorithms in this paper we introduce a new simple strategy into edge searching of a graph which is useful to the various subgraph listing problems applying the strategy we obtain the following four algorithms the first one lists all the triangles in a graph g in o a g m time where m is the number of edges of g and a g the arboricity of g the second finds all the quadrangles in o a g m time since a g is at most three for a planar graph g both run in linear time for a planar graph the third lists all the complete subgraphs k l of order l in o la g l 2 m time the fourth lists all the cliques in o a g m time per clique all the algorithms require linear space we also establish an upper bound on a g for a graph g a g leqq lceil 2m n 1 2 rceil where n is the number of vertices in g

delaunay triangulations in o sort n time and more we present several results about delaunay triangulations dts and convex hulls in transdichotomous and hereditary settings i the dt of a planar point set can be computed in expected time o sort n on a word ram where sort n is the time to sort n numbers we assume that the word ram supports the shuffle operation in constant time ii if we know the ordering of a planar point set in x and in y direction its dt can be found by a randomized algebraic computation tree of expected linear depth iii given a universe u of points in the plane we construct a data structure d for delaunay queries for any p s u d can find the dt of p in expected time o vpv log log vuv iv given a universe u of points in 3 space in general convex position there is a data structure d for convex hull queries for any p s u d can find the convex hull of p in expected time o vpv log log vuv 2 v given a convex polytope in 3 space with n vertices which are colored with g 2 colors we can split it into the convex hulls of the individual color classes in expected time o n log log n 2 the results i iii generalize to higher dimensions where the expected running time now also depends on the complexity of the resulting dt we need a wide range of techniques most prominently we describe a reduction from dts to nearest neighbor graphs that relies on a new variant of randomized incremental constructions using dependent sampling

compact visibility representation of 4 connected plane graphs the visibility representation vr for short is a classical representation of plane graphs the vr has various applications and has been extensively studied in the literature a main focus of the study is to minimize the size of the vr it is known that there exists a plane graph g with n vertices where any vr of g requires a size at least 2n3 x 4n3 3 for upper bounds it is known that every plane graph has a vr with size at most 23n x 2n 5 and a vr with size at most n 1 x 43n it has been an open problem to find a vr with both height and width simultaneously bounded away from the trivial upper bounds namely of size c hnxc wn with c h 1 and c w 2 in this paper we provide the first vr construction for a non trivial graph class that simultaneously bounds both the height and the width we prove that every 4 connected plane graph has a vr with height 3n4 2 n 4 and width 3n2 our vr algorithm is based on an st orientation of 4 connected plane graphs with special properties the area of the vr presented in this paper is larger than the area of some of the previous results for this graph class however bounding one dimension of the vr only requires finding a good st orientation or a good dual s t orientation of g on the other hand bounding both dimensions of the vr requires finding a good st orientation and a good dual s t orientation of g at the same time and hence is far more challenging since the st orientation is a very useful concept in other applications this result may be of independent interest reducing the height the width respectively of the vr is the same as reducing the length of the longest path in an st orientation of g dual st orientation respectively we show that it s np complete to find an st orientation of a 2 connected plane graph that minimizes the sum of the length of the longest path in the orientation and the length of the longest path in its dual orientation

preemptive ensemble motion planning on a tree consider the problem of finding a minimum cost tour to transport a set of objects between the vertices of a tree by a vehicle that travels along the edges of the tree the vehicle can carry only one object at a time and it starts and finishes at the same vertex of the tree it is shown that if objects can be dropped at intermediate vertices along its route and picked up later then the problem can be solved in polynomial time two efficient algorithms are presented for this problem the first algorithm runs in o k qn time where n is the number of vertices in the tree k is the number of objects to be moved and q leq min k n is the number of nontrivial connected components in a related directed graph the second algorithm runs in o k n log n time

random access to grammar compressed strings and trees grammar based compression where one replaces a long string by a small context free grammar that generates the string is a simple and powerful paradigm that captures sometimes with slight reduction in efficiency many of the popular compression schemes including the lempel ziv family run length encoding byte pair encoding sequitur and re pair in this paper we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string let s be a string of length n compressed into a context free grammar mathcal s of size n we present two representations of mathcal s achieving o log n random access time and either o n cdot alpha k n construction time and space on the pointer machine model or o n construction time and space on the ram here alpha k n is the inverse of the k th row of ackermann s function our representations also efficiently support decompression of any substring in s we can decompres

orderly spanning trees with applications we introduce and study orderly spanning trees of plane graphs this algorithmic tool generalizes canonical orderings which exist only for triconnected plane graphs although not every plane graph admits an orderly spanning tree we provide an algorithm to compute an orderly pair for any connected planar graph g consisting of an embedded planar graph h isomorphic to g and an orderly spanning tree of h we also present several applications of orderly spanning trees 1 a new constructive proof for schnyder s realizer theorem 2 the first algorithm for computing an area optimal 2 visibility drawing of a planar graph and 3 the most compact known encoding of a planar graph with o 1 time query support all algorithms in this paper run in linear time

morrey campanato estimates for helmholtz equations abstract we derive uniform weighted l 2 and morrey campanato type estimates for helmholtz equations in a medium with a variable index which is not necessarily constant at infinity our technique is based on a multiplier method with appropriate weights which generalize those of morawetz for the wave equation we also extend our method to the wave equation

on pointers versus addresses summary what is the cost of random access to memory we address this fnndamental problem by studying the simulation of random addressing by a machine which lacks it a pointer machine the model we define allows the use of a data type of our choice a ram program of time i and space s can be simulated in o t log a time using a tree however this is not an obvious lower bound since a high level data type may allow us to encode the data in a more economic way our major contribution is the formalization of incompressibility for general data types the definition extends a similar property 01 strings that underlies the theory of kolmogorov complexity the main theorem states that for all incompressible data types an q t log s lower bound holds incompressibility trivially holds for strings but is harder to prove for a powerlul data type we prove incompressibility for the real numbers with a set of primitives which includes all functions which are continuously differentiable except on a countable closed set this may be the richest set of operations considered in a lower bound proof the prooi relies on the implicit functions theorem and baire s category theorem we also show that the integers with arithmetic x and lz zj any boolean operations and left shift are incompressible the inclusion of right shift reverses the situation and we obtain an o tq s upper bound where s is a functional inverse of ackermann s function

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

efficient seed computation revisited the notion of the cover is a generalization of a period of a string and there are linear time algorithms for finding the shortest cover the seed is a more complicated generalization of periodicity it is a cover of a superstring of a given string and the shortest seed problem is of much higher algorithmic difficulty the problem is not well understood no linear time algorithm is known in the paper we give linear time algorithms for some of its versions computing shortest left seed array longest left seed array and checking for seeds of a given length the algorithm for the last problem is used to compute the seed array of a string i e the shortest seeds for all the prefixes of the string in o n 2 time we describe also a simpler alternative algorithm computing efficiently the shortest seeds as a by product we obtain an o nlog n m time algorithm checking if the shortest seed has length at least m and finding the corresponding seed we also correct some important details missing in the previously known shortest seed algorithm iliopoulos et al 1996 14

send and split method for minimum concave cost network flows many problems from inventory production and capacity planning and from network design exhibit scale economies and can be formulated in terms of finding minimum additive concave cost nonnegative network flows we reduce the problem to an equivalent one in which the arc flow costs are nonnegative and give a dynamic programming method called the send and split method to solve it the main work of the method entails repeatedly solving set splitting and minimum cost chain problems in uncapacitated networks with n nodes a arcs and d 1 demand nodes i e nodes with nonzero exogenous demand the algorithm requires up to n2 13d s2d operations additions and comparisons where s n log2n 3a is the number of operations required to solve a minimum cost chain problem with nonnegative arc costs on the augmented graph formed by appending a node and an arc thereto from each node in the graph if also the network is k planar i e the graph is planar with all demand nodes lying on the boundary of k faces the method requires at most n2 kd3k sd2k operations the algorithm can be applied to capacitated networks because they can be reduced to equivalent uncapacitated ones these results unify significantly generalize e g to cyclic problems and sometimes improve upon e g for tandem facilities known polynomial time dynamic programming algorithms for wagner and whitin s wagner h m whitin t m 1958 dynamic version of the economic lot size model management sci 5 89 96 dynamic economic order quantity problem zangwill s zangwill w i 1969 a backlogging model and a multi echelon model of a dynamic economic lot size production system a network approach management sci 15 506 527 generalization to tandem facilities and veinott s veinott jr a f 1969 minimum concave cost solution of leontief substitution models of multi facility inventory systems oper res 17 262 291 increasing capacity warehousing problem the networks for the finite period versions of these problems are each 1 planar the method improves upon zangwill s zangwill w i 1968 minimum concave cost flows in certain networks management sci 14 429 450 related oand running time dynamic programming method for finding minimum additive concave cost non negative flows in circuitless single source networks we also implement the method to solve in polynomial time the d 1 demand node and k planar versions of the minimum cost forest and steiner problems in graphs the running time for the d 1 demand node steiner problem in graphs is comparable to that of dreyfus and wagner s dreyfus s e wagner r a 1971 the steiner problem in graphs networks1 195 207 method

map graphs we consider a modified notion of planarity in which two nations of a map are considered adjacent when they share any point of their boundaries not necessarily an edge as planarity requires such adjacencies define a map graph we give an np characterization for such graphs derive some consequences regarding sparsity and coloring and survey some algorithmic results

linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method abstract in the present study we apply the natural mode method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures in this context we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations which constitute basic elements of the method of intelligent physical lumping subsequently we present the ariban scheme accumulation of the rigid body and natural modes for geometrically nonlinear analysis it is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly in addition the structure of the algorithm and its matrix language are ideally suited for modern parallel computers we conclude our study with numerical examples for isotropic and composite plates all the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations

constrained floorplans in 2d and 3d a rectilinear dual of a plane graph refers to a partition of a rectangular area into nonoverlapping rectilinear polygonal modules where each module corresponds to a vertex such that two modules have a side contact iff their corresponding vertices are adjacent an interesting observation is that most algorithms yielding low polygonal complexity rectilinear duals require the use of shape modules or their extensions to justify the intuition that shape modules are more powerful than other 8 sided modules we show the optimum polygonal complexity of free rectilinear duals to be exactly 12 our construction uses only monotone staircase modules we continue this line of research by studying polygonal complexity and area universality of rectilinear duals using modules of constrained shapes motivated by the design challenges in 3d ic technology we also study the generalization of rectilinear duals in three dimensions by allowing each module to be an orthogonal polyhedron such a generalization to three dimensions opens the door for non planar graphs to be accommodated in floorplan design in particular we prove that all chordal graphs admit 3d floorplans which parallels the well known result that all maximal plane graphs admit rectilinear duals

free vibration analysis of multilayered composite plates and shells with the natural approach abstract natural curved triangular shell element natcop developed in 1 is employed to vibration mode analysis of multilayered composite plates and shells the shells can be either symmetric or unsymmetric the spectral transformation lanczos method with selective or full orthogonalization is used to solve the eigenvalue problem of a pencil k m proper shifting of the eigenvalues is essential for the success of this method certain problems associated with the shift are discussed several numerical examples including symmetric and unsymmetric composite plates and unsymmetric composite conical shells are tested and show that element natcop is also efficient and reliable for free vibration analysis

efficient algorithms for shortest partial seeds in words abstract a factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w a factor u is a seed of w if it is a cover of a superstring of w covers and seeds extend the classical notions of periodicity we introduce a new notion of partial seed that is a factor covering as a seed at least positions in a given word we use the cover suffix tree recently introduced in the context of partial covers kociumaka et al 2015 13 an o n log n time algorithm constructing such a tree is known however it appears that partial seeds are more complicated than partial covers our algorithms require algebraic manipulations of special functions related to edges of the modified cover suffix tree and the border array we present a procedure for computing shortest partial seeds that works in o n time if the cover suffix tree is already given this is a full version which includes all the proofs of a paper that appeared at cpm 2014 1

on line planarity testing the on line planarity testing problem consists of performing the following operations on a planar graph g i testing if a new edge can be added to g so that the resulting graph is itself planar ii adding vertices and edges such that planarity is preserved an efficient technique for on line planarity testing of a graph is presented that uses o n space and supports tests and insertions of vertices and edges in o log n time where n is the current number of vertices of g the bounds for tests and vertex insertions are worst case and the bound for edge insertions is amortized we also present other applications of this technique to dynamic algorithms for planar graphs

tight bounds on the solutions of multidimensional divide and conquer maximin recurrences abstract in this paper upper bounds are presented for the solution of the following multidimensional divide and conquer maximin recurrence g n max n 1 n 2 n p n n 1 n 2 n p 1 i 1 p g n i smin 1 i p k f n i where p 2 1 k f is an arbitrary nondecreasing function and smin 1 i p k f n i denotes the sum of the smallest k numbers among f n 1 f n 2 and f n p all the presented upper bounds are at most log 2 k p times the exact solution of g n the derivation of the upper bounds is based on properties of partition trees for k 1 and k p 1 we obtain respectively two of the recurrences previously studied by alonso et al siam j discrete math 8 1995 428 447 in both of these two cases our results improve theirs

an efficient algorithm for sequence comparison with block reversals given two sequences x and y that are strings over some alphabet set we consider the distance d x y between them defined to be minimum number of character replacements and block substring reversals needed to transform x to y or vice versa the operations are required to be disjoint this is the simplest sequence comparison problem we know of that allows natural block edit operations block reversals arise naturally in genomic sequence comparison they are also of interest in matching music data we present an algorithm for exactly computing the distance d x y it takes time o x log2 x and hence is near linear trivial approach takes quadratic time

string matching with weighted errors abstract in the approximate string matching problem differences are allowed between the pattern string p and each of its occurrences in the text string t and one is interested in finding all the occurrences of p in t with at most k differences we consider here weighted differences errors between p and t and develop fast sequential and parallel algorithms in particular we allow the following types of errors mismatch whose weight depends on the mismatching characters extra character with constant weight missing character with constant weight and transposition of two consecutive characters with constant weight a set of theoretical results allows to extend known algorithms to solve this problem with o kn sequential time and o k log m parallel time on a 4pram model with max n k 1 mp2 processors where k is the maximum sum of the error weights n is the length of t and m is the length of p

swapping a failing edge of a shortest paths tree by minimizing the average stretch factor we consider a two edge connected undirected graph g v e with n nodes and m non negatively real weighted edges and a single source shortest paths tree spt t of g rooted at an arbitrary node r if an edge in t is temporarily removed it makes sense to reconnect the nodes disconnected from the root by adding a single non tree edge called a swap edge instead of rebuilding a new optimal spt from scratch in the past several optimality criteria have been considered to select a best possible swap edge in this paper we focus on the most prominent one that is the minimization of the average distance between the root and the disconnected nodes to this respect we present an o mlog2n time and o m space algorithm to find a best swap edge for every edge of t thus improving for m o n2 log2n the previously known o n2 time and space complexity algorithm

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors

verification and sensitivity analysis of minimum spanning trees in linear time komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree the total computational work required by his method is much larger than linear however this paper describes a linear time algorithm for verifying a minimum spanning tree this algorithm combines the result of komlos with a preprocessing and table look up method for small subproblems and with a previously known almost linear time algorithm additionally an optimal deterministic algorithm and a linear time randomized algorithm for sensitivity analysis of minimum spanning trees are presented

algorithms for finding the weight constrained k longest paths in a tree and the length constrained k maximum sum segments of a sequence in this work we obtain the following new results given a tree t v e with a length function e r and a weight function w e r a positive integer k and an interval l u the weight constrainedklongest paths problem is to find the k longest paths among all paths in t with weights in the interval l u we show that the weight constrainedklongest paths problem has a lower bound w vlogv k in the algebraic computation tree model and give an o vlogv k time algorithm for it given a sequence a a 1 a 2 a n of numbers and an interval l u we define the sum and length of a segment a i j to be a i a i 1 a j and j i 1 respectively the length constrainedkmaximum sum segments problem is to find the k maximum sum segments among all segments of a with lengths in the interval l u we show that the length constrainedkmaximum sum segments problem can be solved in o n k time