efficient algorithms for the inverse spanning tree problem the inverse spanning tree problem is to modify edge weights in a graph so that a given treet is a minimum spanning tree the objective is to minimize the cost of the deviation the cost of deviation is typically a convex function we propose algorithms here that are faster than all known algorithms for the problem our algorithm s run time for any convex inverse spanning tree problem iso nm log 2n for a graph onn nodes andm edges plus the time required to find the minima of then convex deviation functions this not only improves on the complexity of previously known algorithms for the general problem but also for algorithms devised for special cases for the case when the objective is weighted absolute deviation sokkalingam et al 1999 devised an algorithm with run timeo n2m log nc forc the maximum edge weight for the sum of absolute deviations our algorithm runs in timeo n2 logn matching the run time of a recent ahuja and orlin 2000 improvement for this case a new algorithm for bipartite matching in path graphs is reported here with complexity ofo n1 5 logn this leads to a second algorithm for the sum of absolute deviations running ino n1 5 logn logc steps

parallel delaunay triangulation in three dimensions abstract a generic parallel delaunay triangulation scheme by means of zonal partition of points is proposed for efficient delaunay triangulation points are first sorted into cells each of which is allocated roughly equal number of points the cells are naturally grouped into zones in which delaunay triangulation is constructed by simultaneous point insertion cell by cell within each zone tetrahedra at the boundary between zones are created in parallel by adding layers of cells at the boundary of each zone to ensure that circumspheres of boundary tetrahedra contain no points in their interior redundant tetrahedra at the boundary between zones can be easily eliminated by individual processors in a completely independent manner by means of the elegant minimum vertex allocation scheme such that a simplex with k vertices from zones z 1 z 2 z k is allocated to zone z min z 1 z 2 z k the parallel 3d delaunay triangulation algorithm has been coded in intel fortran vs2010 the parallel zonal insertion on a pc can boost the speed of the single processor insertion by 4 5 times for the insertion of 50 million randomly generated spatial points in 133 s the scalability of the parallel zonal insertion algorithm has also been tested on a proper multi core machine with 12 processors running on openmp parallel directives with shared memory provided the number of zones is an integral multiple of the number of processors used almost 100 scalability at 90 efficiency was observed for parallel insertion using 2 4 6 8 and 12 processors and a 10 8 time speed up was recorded in a parallel insertion of 20 million points in 2 2 3 12 zones by 12 processors

a technique for speeding up the solution of the lagrangian dual we propose techniques for the solution of the lp relaxation and the lagrangean dual in combinatorial optimization and nonlinear programming problems our techniques find the optimal solution value and the optimal dual multipliers of the lp relaxation and the lagrangean dual in polynomial time using as a subroutine either the ellipsoid algorithm or the recent algorithm of vaidya moreover in problems of a certain structure our techniques find not only the optimal solution value but the solution as well our techniques lead to significant improvements in the theoretical running time compared with previously known methods interior point methods ellipsoid algorithm vaidya s algorithm we use our method to the solution of the lp relaxation and the langrangean dual of several classical combinatorial problems like the traveling salesman problem the vehicle routing problem the steiner tree problem thek connected problem multicommodity flows network design problems network flow problems with side constraints facility location problems k polymatroid intersection multiple item capacitated lot sizing problem and stochastic programming in all these problems our techniques significantly improve the theoretical running time and yield the fastest way to solve them

improvement on the 10 node tetrahedral element for three dimensional problems by decomposing the strain part of the conforming 10 node tetrahedral element t10 and relaxing the compatibility condition for the constant strain term the performance of the element can be improved by introducing the incompressible condition in the high order strain term the element can be made very efficient for the analysis of the nearly incompressible problem numerical results show that the modified element in general has better accuracy and reliability compared to the classical displacement based tetrahedral element t10 for a wide range of structural problems including the analysis of thin and slender structures

chemotaxis driven pattern formation for a reaction diffusion chemotaxis model with volume filling effect in this paper we analytically and numerically investigate the emerging process of pattern formation for a reaction diffusion chemotaxis model with volume filling effect we first apply globally asymptotic stability analysis to show that the chemotactic flux is the key mechanism for pattern formation then by weakly nonlinear analysis with multiple scales and the adjoint system theory we derive the cubic and the quintic stuart landau equations to describe the evolution of the amplitude of the most unstable mode and thus the analytical approximate solutions of the patterns are obtained next we present the selection law of principal wave mode of the emerging pattern by considering the competition of the growing modes and for this we deduce the change rule of the most unstable mode and the coupled ordinary differential equations that indicates the significant nonlinear interaction of two competing modes finally in the subcritical case we clarify that there exists the phenomenon of hysteresis which implies the existence of large amplitude pattern for the bifurcation parameter values smaller than the first bifurcation point therefore we answer the open problems proposed in the known references and improve some of results obtained there all the theoretical results are tested against the numerical results showing excellent qualitative and good quantitative agreement

boundary recovery for three dimensional conforming delaunay triangulation we present an efficient boundary recovery method for conforming delaunay triangulation of three dimensional domains our method combines local transformations like edges faces swappings and modified constrained delaunay refinement like edges faces splittings to recover the missing boundary edges and faces its convergence is theoretically proved its effectiveness is also demonstrated through some meshing examples

generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3d domain this paper describes an algorithm for the generation of tetrahedral mesh of specified element size over an unbounded three dimensional domain starting from an arbitrary point in space defined as the origin and guided by the concept of advancing front spheres of size compatible with the specified element size are packed tightly together one by one to form a cluster of spheres of different sizes the compactness of the cluster of spheres is achieved by packing spheres at a site closest to the origin in a densest manner with tangent but no overlapping with as many other spheres as possible in view of these criteria a rotational mechanism between spheres is innovated which allows the newly inserted sphere to follow the path by rotation between existing spheres until the lowest point is reached the centres of the packing spheres provide ideal locations for delaunay point insertion to form a triangulation of tetrahedral elements of size compatible with the specified value spheres of random size distribution or of size specified by a node spacing function are packed by the proposed algorithm in all test examples high quality tetrahedral elements of size consistent with the specified node spacing are generated the process is fast and robust and the time complexity for mesh generation is expected to be almost linear however in the present implementation a quasi linear time relationship is observed as a search for the nearest node on the front is proposed in the sphere packing process the memory requirement has been kept to a minimum as no additional data structure other than the adjacency relationship of the tetrahedral elements as required by the delaunay triangulation is stored the structure of the advancing frontal surface needs not be explicitly constructed nor updated as it is simply not required in the sphere packing process

improved algorithms for bipartite network flow in this paper network flow algorithms for bipartite networks are studied a network g v e is called bipartite if its vertex set v can be partitioned into two subsets v 1 and v 2 such that all edges have one endpoint in v 1 and the other in v 2 let n v n 1 v 1 n 2 v 2 m e and assume without loss of generality that n 1 leq n 2 a bipartite network is called unbalanced if n 1 ll n 2 and balanced otherwise this notion is necessarily imprecise it is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks the basic idea in these improvements is a two edge push rule that allows one to charge most computation to vertices in v 1 and hence develop algorithms whose running times depend on n 1 rather than n for example it is shown that the two edge push version of goldberg and tarjan s fifo preflow push algorithm runs in o n 1 m n 1 3 time and that the analogous version of ahuja and orlin s excess scaling algorithm runs in o n 1 m n 1 2 log u time where u is the largest edge capacity these ideas are also extended to dynamic tree implementations parametric maximum flows and minimum cost flows

global attractor for a chemotaxis model with prevention of overcrowding abstract chemotaxis model with volume filling introduced by painter and hillen is studied under no flux or dirichlet boundary conditions existence of global in time solution to a full model is proved for some cases existence of a global attractor in the space w 1 p r 2 p n r n is shown

structural and algorithmic properties for parametric minimum cuts we consider the minimum s t cut problem in a network with parametrized arc capacities following the seminal work of gallo et al siam j comput 18 1 30 55 1989 classes of this parametric problem have been shown to enjoy the nice structural property that minimum cuts are nested and the nice algorithmic property that all minimum cuts can be computed in the same asymptotic time as a single minimum cut by using a clever flow update step to move from one value of the parameter to the next we present a general framework for parametric minimum cuts that extends and unifies such results we define two conditions on parametrized arc capacities that are necessary and sufficient for strictly decreasing differences of the parametric cut function known results in parametric submodular optimization then imply the structural property we show how to construct appropriate flow updates in linear time under the above conditions implying that the algorithmic property also holds under these conditions we then consider other classes of parametric minimum cut problems without decreasing differences for which we establish the structural and or the algorithmic property as well as other cases where nested minimum cuts arise

adjoint a posteriori error measures for anisotropic mesh optimisation in this paper an adjoint or sensitivity based error measure is formulated which measures the error contribution of each solution variable to an overall goal the goal is typically embodied in an integral functional e g the solution in a small region of the domain of interest the resulting a posteriori error measures involve the solution of both primal and adjoint problems a comparison of a number of important a posteriori error measures is made in this work there is a focus on developing relatively simple methods that refer to information from the discretised equation sets often readily accessible in simulation codes and do not explicitly use equation residuals this method is subsequently used to guide anisotropic mesh adaptivity of tetrahedral finite elements mesh adaptivity is achieved here with a series of optimisation heuristics of the landscape defined by mesh quality mesh quality is gauged with respect to a riemann metric tensor embodying an a posteriori error measure such that an ideal element has sides of unit length when measured with respect to this metric tensor this results in meshes in which each finite element node has approximately equal subject to certain boundary conforming constraints and the performance of the mesh optimisation heuristics error contribution to the functional goal

a strongly polynomial algorithm for the transportation problem for the linear transportation problem withm supply nodes n demand nodes andk feasible arcs we describe an algorithm which runs in time proportional tom logm k n logn assuming w l o g m n the algorithm uses excess scaling the complexity bound is a slight improvement over the bound achieved by an application of a min cost flow algorithm of orlin to the transportation problem

solving inverse spanning tree problems through network flow techniques given a solution x and an a priori estimated cost vector c the inverse optimization problem is to identify another cost vector d so that x is optimal with respect to the cost vector d and its deviation from c is minimum in this paper we consider the inverse spanning tree problem on an undirected graph g n a with n nodes and m arcs and where the deviation between c and d is defined by the rectilinear distance between the two vectors that is l1 norm we show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network g0 n0 a0 with math not displayed and math not displayed the bipartite ne twork satisfies the property that n1 n 1 n2 m n 1 and a0 o nm in general n1 n2 using this special structure of the assignment problem we develop a specific implementation of the successive shortest path algorithm that runs in o n3 time we also consider the weighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the weighted deviations of arcs the weighted inverse spanning tree can be formulated as the dual of the transportation problem using a cost scaling algorithm this transportation problem can be solved in o n2m log nc time where c denotes the largest arc cost in the data finally we consider a minimax version of the inverse spanning tree problem and show that it can be solved in o n2 time

constrained boundary recovery for three dimensional delaunay triangulations summary a new constrained boundary recovery method for three dimensional delaunay triangulations is presented it successfully resolves the difficulties related to the minimal addition of steiner points and their good placement applications to full mesh generation are discussed and numerical examples are provided to illustrate the effectiveness of guaranteed recovery procedure copyright 2004 john wiley sons ltd

lower bounds for the earliness tardiness scheduling problem on parallel machines with distinct due dates this paper addresses the parallel machine scheduling problem in which the jobs have distinct due dates with earliness and tardiness costs new lower bounds are proposed for the problem they can be classed into two families first two assignment based lower bounds for the one machine problem are generalized for the parallel machine case second a time indexed formulation of the problem is investigated in order to derive efficient lower bounds throught column generation or lagrangean relaxation a simple local search algorithm is also presented in order to derive an upper bound computational experiments compare these bounds for both the one machine and parallel machine problems and show that the gap between upper and lower bounds is about 1 5

approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non identical capacities abstract we consider the problem of scheduling jobs with release times and arbitrary sizes on batch machines with non identical capacities to minimize makespan a job can only be assigned to a machine whose capacity is not less than the size of the job a machine can process a group of jobs as a batch simultaneously as long as the total size of the jobs in this batch does not exceed the capacity of the machine the processing time of a batch is equal to the longest processing time of all the jobs in the batch for the case of equal release times we obtain a fast 5 approximation algorithm as well as an algorithm with approximation ratio arbitrarily close to 2 for the case of unequal release times and a fixed number of different batch capacities we obtain an algorithm with approximation ratio arbitrarily close to 2 we also study the problem of scheduling jobs with equal release times arbitrary sizes inclusive processing set restrictions and incompatible families on batch machines with identical capacities to minimize makespan we obtain a 8 3 approximation algorithm as well as an algorithm with approximation ratio arbitrarily close to 2 if only a single family is considered a 2 approximation algorithm is presented it is likely that these results cannot be too substantially improved upon since all of the problems studied cannot be approximated to within a ratio smaller than 2 unless p np

polynomial time algorithms for ratio regions and a variant of normalized cut in partitioning clustering and grouping problems a typical goal is to group together similar objects or pixels in the case of image processing at the same time another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large these goals are often combined as a ratio optimization problem one example of such a problem is a variant of the normalized cut problem another is the ratio regions problem we devise here the first polynomial time algorithms solving optimally the ratio region problem and the variant of normalized cut as well as a few other ratio problems the algorithms are efficient and combinatorial in contrast with nonlinear continuous approaches used in the image segmentation literature which often employ spectral techniques such techniques deliver solutions in real numbers which are not feasible to the discrete partitioning problem furthermore these continuous approaches are computationally expensive compared to the algorithms proposed here the algorithms presented here use as a subroutine a minimum s t cut procedure on a related graph which is of polynomial size the output consists of the optimal solution to the respective ratio problem as well as a sequence of nested solutions with respect to any relative weighting of the objectives of the numerator and denominator

anisotropic centroidal voronoi tessellations and their applications in this paper we introduce a novel definition of the anisotropic centroidal voronoi tessellation acvt corresponding to a given riemann metric tensor a directional distance function is used in the definition to simplify the computation we provide algorithms to approximate the acvt using the lloyd iteration and the construction of anisotropic delaunay triangulation under the given riemannian metric the acvt is applied to the optimization of two dimensional anisotropic delaunay triangulation to the generation of surface cvt and high quality triangular mesh on general surfaces various numerical examples demonstrating the effectiveness of the proposed method are presented

basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth recently wang and hillen chaos 17 3 2007 037108 037108 introduced a modified keller segel model with logistic growth that exhibits complex spatiotemporal dynamics of spikes these dynamics are driven by merging of spikes on one hand and spike insertion on the other in this paper we analyse the basic mechanisms that initiate and sustain these events we identify two distinguished regimes in the first regime a single interior spike drifts towards a boundary this instability is responsible for spike merging the same regime further exhibits spike insertion we identify a fold point bifurcation which is precursor to spike insertion event in the second regime we show that it is possible to stabilize a single interior spike and we compute analytically a critical threshold which is responsible for spike stabilization in particular our calculation characterizes a stable spike in the keller segel model with logistic growth this is in contrast to the classical keller segel model where the interior spike is known to be unstable

stationary solutions of a volume filling chemotaxis model with logistic growth and their stability in this paper we derive the conditions for the existence of stationary solutions i e nonconstant steady states of a volume filling chemotaxis model with logistic growth over a bounded domain subject to homogeneous neumann boundary conditions at the same time we show that the same system without the chemotaxis term does not admit pattern formations moreover based on an explicit formula for the stationary solutions which is derived by asymptotic bifurcation analysis we establish the stability criteria and find a selection mechanism of the principal wave modes for the stable stationary solution by estimating the leading term of the principal eigenvalue we show that all bifurcations except the one at the first location of the bifurcation parameter are unstable and if the pattern is stable then its principal wave mode must be a positive integer which minimizes the bifurcation parameter for a special case where the carrying capacity is one half we find a necessary and sufficient condition for th

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

variational surface reconstruction based on delaunay triangulation and graph cut a novel method for surface reconstruction from an unorganized point set is presented an energy functional based on a weighted minimal surface model is proposed for surface reconstruction which is efficiently minimized by graph cut methods by solving the minimization problem on the graph dual to a delaunay based tetrahedral mesh the advantages of explicit and implicit methods for surface reconstruction are well integrated a triangular surface mesh homeomorphic to the original surface can be extracted directly from the tetrahedral mesh provided a sufficient sampling density exists difficult cases involving undersampling non uniformity noises and topological complexities can be handled effectively as well furthermore for the first time multi phase surface reconstruction is realized based on the graph cut methods various examples are included for demonstrating the efficiency and effectiveness of the proposed method copyright 2010 john wiley sons ltd

approximability issues for unconstrained and constrained maximization of half product related functions we address the boolean programming problem of maximizing a half product function with and without a linear knapsack constraint maximizing the half product can be done in polynomial time adding a knapsack constraint makes the problem non approximable within a constant factor provided that the coefficients in the linear part of the function are negative for maximizing a function with positive coefficients in the linear part we develop a fully polynomial time approximation scheme

spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law in this paper a reaction diffusion bimolecular model with autocatalysis and saturation law is investigated firstly we provide some conditions for the stability turing instability of the constant positive solution then we mainly consider hopf bifurcations and steady state bifurcations which bifurcate from the unique constant positive solution of the system our results suggest the existence of spatially non homogeneous periodic orbit and non constant positive steady state solutions which implies the possibility of rich spatiotemporal patterns in this diffusive bimolecular model numerical examples are presented to support our theoretical analysis furthermore non existence of non constant steady state is investigated in terms of parameters

3d hybrid mesh generation for reservoir simulation a great challenge for flow simulators of new generation is to gain more accuracy at well proximity within complex geological structures for this purpose a new approach based on hybrid mesh modelling was proposed in 2d by balaven et al proceedings of the 7th international conference on numerical grid generation in computational field simulations whistler canada 2000 407 416 in this hybrid mesh the reservoir is described by a structured quadrilateral mesh and drainage areas around wells are represented by radial circular meshes in order to generate a global conforming mesh unstructured transition meshes constituted by convex polygonal elements satisfying finite volume properties are used to connect these two structured meshes the hybrid mesh allows us to take full advantage of the simplicity and practical aspects of structured meshes while complexity inherent to unstructured meshes is introduced only where strictly needed this paper presents the 3d extension of the generation of such a hybrid mesh eccomas jyvaskyla finland 2004 the proposed method uses 3d power diagrams to generate the transition mesh due to the round off errors this mesh is modified in order to ensure the conformity with the structured meshes in addition some criteria are introduced to measure the mesh quality as well as an optimization procedure to remove or to expand small edges of the transition mesh under finite volume properties constraints numerical results are given to show the efficiency of the approach copyright 2005 john wiley sons ltd

optimal attack and reinforcement of a network in a nonnegative edge weighted network the weight of an edge represents the effort required by an attacker to destroy the edge and the attacker derives a benefit for each new component created by destroying edges the attacker may want to minimize over subsets of edges the difference between or the ratio of the effort incurred and the benefit received this idea leads to the definition of the strength of the network a measure of the resistance of the network to such attacks efficient algorithms for the optimal attack problem the problem of computing the strength and the problem of finding a minimum cost reinforcement to achieve a desired strength are given these problems are also solved for a different model in which the attacker wants to separate vertices from a fixed central vertex

optimal delaunay point insertion summary an efficient algorithm for delaunay triangulation of a given set of points in d dimensions is presented various steps of the point insertion algorithm are reviewed and many acceleration procedures are implemented to speed up the triangulation process new features include the search for a neighbouring point by a layering scheme locating the containing simplex by a random walk formulas of important geometrical quantities of a new simplex based on those of an old one a novel approach in establishing the adjacency relationship using connection matrices the resulting scheme seems to be one of the fastest triangulation algorithms known which enables us to generate tetrahedra in r3 with a linear generation rate of 15 ooo tetrahedra per second for randomly generated points on an hp 735 workstation

3d delaunay mesh generation coupled with an advancing front approach abstract this paper describes a fully automatic mesh generation method suitable for domains of any shape in r 3 initially a so called boundary mesh is generated wherein internal points are created using advancing front point placement and inserted using a delaunay method the algorithm combines the advantages of efficiency and nice mathematical properties of a delaunay approach with advancing front high quality point placement strategy several three dimensional examples are presented to demonstrate the overall efficiency and the relevance of the combined procedure the present method can be extended to isotropic or anisotropic adaptive mesh generation

generation of finite element mesh with variable size over an unbounded 2d domain with the advance of the finite element general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled this paper describes an algorithm for the generation of finite element mesh of variable element size over an unbounded 2d domain by using the advancing front circle packing technique unlike the conventional frontal method the procedure does not start from the object boundary but starts from a convenient point within an open domain the sequence of construction of the packing circles is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation as soon as a circle is added to the generation front finite elements are directly generated by properly connecting frontal segments with the centre of the new circle in contrast to other mesh generation schemes the domain boundary is not considered in the process of circle packing this reduces a lot of geometrical checks for intersection with frontal segments and a linear time complexity for mesh generation can be achieved in case the boundary of the domain is needed simply generate an unbounded mesh to cover the entire object as the element adjacency relationship of the mesh has already been established in the circle packing process insertion of boundary segments by neighbour tracing is fast and robust details of such a boundary recovery procedure are described and practical meshing problems are given to demonstrate how physical objects are meshed by the unbounded meshing scheme followed by the insertion of domain boundaries

tetrahedral mesh optimisation and adaptivity for steady state and transient finite element calculations abstract a method for optimising a pre existing mesh of tetrahedral finite elements is described it is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality a riemannian metric reflecting the a posteriori error measure is used to calculate element size and shape a functional is defined which embodies both shape and size quality of an element with respect to the metric and is used to gauge mesh quality a heuristic based local search strategy is adopted local in the sense that it has no hill climbing abilities the paper presents applications of the method to complex steady state and time dependent problems which highlight its anisotropic feature capturing abilities numerical evidence is provided which suggests that the computational complexity time of the proposed algorithm varies linearly with the number of elements or nodes of the finite element mesh

an efficient cost scaling algorithm for the assignment problem the cost scaling push relabel method has been shown to be efficient for solving minimum cost flow problems in this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment s special structure the results show that the method is very promising for practical use

algorithms for distributing telecommunication traffic on a multiple ring sonet based network abstract we examine a problem arising in the assignment of telecommunication traffic to a set of synchronous optical network sonet rings prior sonet design algorithms determine node to ring assignments while concurrently prescribing an assignment of traffic to the rings however due to uncertain voice and data demand among client nodes it may become necessary to revise the planned routing scheme once the true values of this data are realized we develop a minimum cost flow algorithm for the case in which demands may be split across multiple rings and provide a transformation to a maximum flow problem for specially structured data the case in which each demand pair may be routed on only one ring is proven to be np hard and we accordingly provide a powerful heuristic and an effective standard valid inequality generation scheme to optimally solve this problem within reasonable computational limits the effectiveness of our approach is demonstrated on a set of randomly generated test data

computing the strength of a graph the strength of a graph is a measure of its vulnerability strictly generalizing the edge connectivity of a weighted graph cunningham j assoc comput mach 32 1985 pp 549 562 showed how to compute the strength of a graph in o v 4 e time using ideas from polymatroids and network flow in this paper his polymatroid approach is modified a modified version of the goldberg tarjan network flow algorithm j assoc comput mach 4 1988 pp 136 146 is used then using ideas developed by gallo grigoriadis and tarjan siam j comput 18 1989 pp 30 55 and by gusfield martel and fernandez baca in siam j comput 16 1987 pp 237 251 it is shown that the solution runs in o v 3 e time analogous speedups for sparse case bounds are also obtainable

spatio temporal chaos in a chemotaxis model abstract in this paper we explore the dynamics of a one dimensional keller segel type model for chemotaxis incorporating a logistic cell growth term we demonstrate the capacity of the model to self organise into multiple cellular aggregations which according to position in parameter space either form a stationary pattern or undergo a sustained spatio temporal sequence of merging two aggregations coalesce and emerging a new aggregation appears this spatio temporal patterning can be further subdivided into either a time periodic or time irregular fashion numerical explorations into the latter indicate a positive lyapunov exponent sensitive dependence to initial conditions together with a rich bifurcation structure in particular we find stationary patterns that bifurcate onto a path of periodic patterns which prior to the onset of spatio temporal irregularity undergo a periodic doubling sequence based on these results and comparisons with other systems we argue that the spatio temporal irregularity observed here describes a form of spatio temporal chaos we discuss briefly our results in the context of previous applications of chemotaxis models including tumour invasion embryonic development and ecology

efficient three dimensional delaunay triangulation with automatic point creation and imposed boundary constraints a method is described which constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra will be produced statistics of measures of grid quality are presented for several grids the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities

long time behaviour of solutions to a chemotaxis model with volume filling effect the lyapunov functional is constructed for a quasilinear parabolic system which models chemotaxis and takes into account a volume filling effect for some typical case it is proved that the limit set of any trajectory consists of regular stationary solutions some lower and upper bounds on the stationary solutions are found for a given range of parameters there are stationary solutions which are inhomogeneous in space

new algorithms for maximum weight matching and a decomposition theorem we revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights we present an algorithm that operates by decomposing the problem into w unweighted versions of the problem where w is the largest edge weight our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when w is small one of the highlights of our algorithm is that it also produces an integral optimal dual solution thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed our algorithm yields a new proof to the total dual integrality of edmonds matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs we also consider the maximum weight capacitated b matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed i

tetrahedral mesh generation and optimization based on centroidal voronoi tessellations the centroidal voronoi tessellation based delaunay triangulation cvdt provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high quality mesh in this paper we discuss algorithms for the construction of the constrained cvdt from an initial delaunay tetrahedral mesh of a three dimensional domain by establishing an appropriate relationship between the density function and the specified sizing field and applying the lloyd s iteration the constrained cvdt mesh is obtained as a natural global optimization of the initial mesh simple local operations such as edges faces flippings are also used to further improve the cvdt mesh several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method copyright 2003 john wiley sons ltd

qualitative analysis of a prey predator model with stage structure for the predator in this paper we propose a diffusive prey predator model with stage structure for the predator we first analyze the stability of the nonnegative steady states for the reduced ode system and then study the same question for the corresponding reaction diffusion system with homogeneous neumann boundary conditions we find that a hopf bifurcation occurs in the ode system but no turing pattern happens in the reaction diffusion system however when a natural cross diffusion term is included in the model we can prove the emergence of stationary patterns i e nonconstant positive stationary solutions for this system moreover these stationary patterns do not exist in the considered parameter regime when there is no cross diffusion

distributed asynchronous relaxation methods for convex network flow problems we consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment the dual of this problem is unconstrained differentiable and well suited for solution via gauss seidel relaxation we show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by several processors in arbitrary order and with arbitrarily large interprocessor communication delays

pattern formation for a two dimensional reaction diffusion model with chemotaxis abstract this paper is devoted to study the formation of stationary patterns for a chemotaxis model with nonlinear diffusion and volume filling effect over a bounded rectangular domain by using linear stability analysis around the homogeneous steady states we establish conditions for the existence of unstable mode bands that lead to the formation of spatial patterns we derive the stuart landau equations for the pattern amplitudes by means of weakly nonlinear multiple scales analysis and fredholm theory in particular we find asymptotic expressions for a wide range of patterns sustained by the system these patterns include mixed mode square hexagonal and roll stationary configurations our analytical results are corroborated by direct simulations of the underlying chemotaxis system

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

bifurcation and stability analysis of steady states to a brusselator model abstract in this paper we consider the structure of the nonnegative steady state solutions of a brusselator model we prove the existence and boundedness of continua of the steady state solutions by applying the theorems of global bifurcation theory the concentration of one intermediary reactant is treated as a bifurcation parameter through the asymptotic bifurcation analysis we derive an explicit formula for the non constant steady states i e stationary patterns using it as a base we establish the stability criteria and find a selection mechanism of the wave modes for the stable patterns by computing the leading term of the principal eigenvalue our results demonstrate that all of the bifurcations other than the one at the first bifurcation location are unstable and if the pattern is stable then its mode must be a positive integer which minimizes the bifurcation parameter a specific example is presented to illustrate our analytical results

the geometric maximum traveling salesman problem we consider the traveling salesman problem when the cities are points in n x211d d for some fixed d and distances are computed according to geometric distances determined by some norm we show that for any polyhedral norm the problem of finding a tour of maximum length can be solved in polynomial time if arithmetic operations are assumed to take unit time our algorithms run in time o nf 2 log n where f is the number of facets of the polyhedron determining the polyhedral norm thus for example we have o n2 log n algorithms for the cases of points in the plane under the rectilinear and sup norms this is in contrast to the fact that finding a minimum length tour in each case is np hard our approach can be extended to the more general case of quasi norms with a not necessarily symmetric unit ball where we get a complexity of o n2f 2 log n for the special case of two dimensional metrics with f 4 which includes the rectilinear and sup norms we present a simple algorithm with o n running time the algorithm does not use any indirect addressing so its running time remains valid even in comparison based models in which sorting requires n log n time the basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms complementing the results on simplicity for polyhedral norms we prove that for the case of euclidean distances in n x211d d for d 3 the maximum tsp is np hard this sheds new light on the well studied difficulties of euclidean distances

delaunay s mesh of a convex polyhedron in dimension d application to arbitrary polyhedra this paper presents a method for creating a delaunay triangulation connected to a set of specified points the theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach valid for dimensions 2 and 3 which is simple robust and well adapted to computation convex polyhedral and arbitrary polyhedral situations are introduced

efficient algorithms for robustness in resource allocation and scheduling problems the robustness function of an optimization minimization problem measures the maximum increase in the value of its optimal solution that can be produced by spending a given amount of resources increasing the values of the elements in its input we present efficient algorithms for computing the robustness function of resource allocation and scheduling problems that can be modeled with partition and scheduling matroids for the case of scheduling matroids we give an o m2n2 time algorithm for computing a complete description of the robustness function where m is the number of elements in the matroid and n is its rank for partition matroids we give two algorithms one that computes the complete robustness function in o m log m time and other that optimally evaluates the robustness function at only a specified point