on parallel integer merging the problem of merging two sorted arrays a a1 a2 an1 and b b1 b2 bn2 is considered for input elements that are drawn from a domain of integers 1 s we present an algorithm that runs in o log log log s time using n log log log s crew pram processors optimal speed up and o ns space where n n1 n2 for input elements that are drawn from a domain of integers 1 n we present a second algorithm that runs in o n time where n is the inverse of ackermann s function using n n crew pram processors and linear space this second algorithm is non uniform however it can be made uniform at a price of a certain loss of speed or by using a crcw pram

on the numerical experiments of the cauchy problem for semi linear klein gordon equations in the de sitter spacetime abstract the computational analysis of the cauchy problem for semi linear klein gordon equations in the de sitter spacetime is considered several simulations are performed to show the time global behaviors of the solutions of the equations in the spacetime based on the structure preserving scheme it is remarked that the sufficiently large hubble constant yields the strong diffusion effect which gives the long and stable simulations for the defocusing semi linear terms the reliability of the simulations is confirmed by the preservation of the numerically modified hamiltonian of the equations

global solutions for semilinear klein gordon equations in flrw spacetimes abstract we consider waves which obey the semilinear klein gordon equation propagating in the friedmann lemaitre robertson walker spacetimes the equations in the de sitter and einstein de sitter spacetimes are the important particular cases we show the global in time existence in the energy class of solutions of the cauchy problem

lifespan of solutions to semilinear damping wave equations in de sitter spacetime abstract this paper studies blowup phenomena for two kind of initial value problem of semilinear damping wave equations in de sitter spacetime the first problem comes from the latter problem of conjecture of strauss in de sitter spacetime and the second problem arises from the latter problem of conjecture of glassey in de sitter spacetime we give blowup and lifespan of solutions on those two problems comparing with non damping case established in yan 2018 one can see that the damping term with a positive bounded time dependent coefficient does not effect blowup of solutions meanwhile we establish a new ode blowup result concerning damping term

vibration analysis of liquid filled pipelines with elastic constraints abstract in this paper a transfer matrix method tmm in frequency domain considering fluid structure interaction of liquid filled pipelines with elastic constraints is proposed the time domain equations considering fluid structure interaction are transformed into frequency domain by laplace transformation and then twelve fourth order ordinary differential equations and two second order ordinary differential equations are deduced from the frequency domain equations the results of the fourteen frequency domain equations are assembled into a transfer matrix which represents the motion of a single pipe section combined with point matrices that describe specified boundary conditions an overall transfer matrix for liquid filled pipeline system can be assembled using the method all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number taking into account the longitudinal vibration transverse vibration and torsional vibration the proposed method can be used to analyze the pipelines with bends several numerical examples with different constraints are presented here to illustrate the application of the proposed method the results are validated by measured and simulation data through the numerical examples it is shown that the proposed method is efficient

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

improved deterministic parallel integer sorting abstract we consider the problem of deterministic sorting of integers on a parallel ram pram the best previous result t hagerup 1987 inform and comput 75 39 51 states that n integers of size polynomial in n can be sorted in time o log n on a priority crcw pram with o n log log n log n processors we prove that n integers drawn from a set 0 m 1 can be sorted on an arbitrary crcw pram in time o log n log log n log log m with a time processor product of o n log log m in particular if m n log n o 1 the time and number of processors used are o log n log log n and o n log log n 2 log n respectively this improves the previous result in several respects the new algorithm is faster it works on a weaker pram model and it is closer to optimality for input numbers of superpolynomial size if log log m o log n log log n the new algorithm is optimally fast for any polynomial number of processors and if log log m 1 1 log log n and log log m 0 log n it has optimal speedup relative to the fastest known sequential algorithm the space needed is o nme for arbitrary but fixed e 0 the sorting algorithm derives its speed from a fast solution to a special list ranking problem of possible independent interest the monotonic list ranking problem in monotonic list ranking each list element has an associated key and the keys are known to increase monotonically along the list we show that monotonic list ranking problems of size n can be solved optimally in time o log n log log n we also discuss and attempt to solve some of the problems arising in the precise description and implementation of parallel recursive algorithms as part of this effort we introduce a new pram variant the allocated pram

improved fast integer sorting in linear space we present a fast deterministic algorithm for integer sorting in linear space our algorithm sorts n integers in the range 0 1 2 m 1 in linear space in o n log log n log log log n time when log m log2 n 0 we can further achieve o n log log n time this improves the o n log log n 2 time bound given in m thorup 1998 in proc 1998 acm siam symp on discrete algorithms soda 98 pp 550 555 this result is obtained by combining our new technique with that of thorup s signature sorting a andersson t hagerup s nilsson and r raman 1995 in proc 1995 symposium on theory of computing pp 427 436 a andersson s result 1996 in proc 1996 ieee symp on foundations of computer science pp 135 141 r raman s result 1996 lecture notes in computer science vol 1136 pp 121 137 springer verlag berlin new york and our previous result y han and x shen 1999 in proc 1999 tenth annual acm siam symposium on discrete algorithms soda 99 baltimore md january pp 419 428 are also used for the design of our algorithms we provide an approach and techniques which are totally different from previous approaches and techniques for the problem as a consequence our technique can be extended to apply to nonconservative sorting and parallel sorting our nonconservative sorting algorithm sorts n integers in 0 1 m 1 in time o n log log n 2 log k log log log n using word length k log m n where k log n our erew parallel algorithm sorts n integers in 0 1 m 1 in o log n 2 time and o n log log n 2 log log log n operations provided log m log n 2

parallel depth first search in general directed graphs a directed cycle separator of an n vertex directed graph is a vertex simple directed cycle such that when the vertices of the cycle are deleted the resulting graph has no strongly connected component with more than n 2 vertices it is shown that the problem of finding a directed cycle separator is in randomized nc it is also proved that computing cycle separators and conducting depth first search in directed graphs are deterministically nc equivalent these two results together yield the first randomized nc algorithm for depth first search in general directed graphs

polylog time and near linear work approximation scheme for undirected shortest paths shortest paths computations constitute one of the most fundamental network problems nonetheless known parallel shortest paths algorithms are generally inefficient they perform significantly more work product of time and processors than their sequential counterparts this gap known in the literature as the transitive closure bottleneck poses a long standing open problem our main result is an o mn e 0 s m n1 e 0 work polylog time randomized algorithm that computes paths within 1 o 1 polylog n of shortest from s source nodes to all other nodes in weighted undirected networks with n nodes and m edges for any fixed e 0 0 this work bound nearly matches the o d sm sequential time in contrast previous polylog time algorithms required nearly min o d n3 o d m2 work even when s 1 and previous near linear work algorithms required near o n time we also present faster sequential algorithms that provide good approximate distances only between distant vertices we obtain an o m sn n e 0 time algorithm that computes paths of weight 1 o 1 polylog n dist o w max polylog n where dist is the corresponding distance and w max is the maximum edge weight our chief instrument which is of independent interest are efficient constructions of sparse hop sets a d e hop set of a network g v e is a set e of new weighted edges such that mimimum weight d edge paths in v e e have weight within 1 e of the respective distances in g we construct hop sets of size o n1 e 0 where e o 1 polylog n and d o polylog n

a polynomial dual simplex algorithm for the generalized circulation problem this paper presents a polynomial time dual simplex algorithm for the generalized circulation problem an efficient implementation of this algorithm is given that has a worst case running time of o m2 m nlogn logb where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the rational gain factors and integral capacities in the network this running time is as fast as the running time of any combinatorial algorithm that has been proposed thus far for solving the generalized circulation problem

bipartite perfect matching is in quasi nc we show that the bipartite perfect matching problem is in quasi mathsf nc 2 that is it has uniform circuits of quasi polynomial size n o log n and o log 2 n depth previously only

parallel search algorithms for graphs and trees abstract this paper surveys parallel algorithms for tree traversal and graph search techniques the principal model of computation considered here is the parallel random access machine in this model each processor can access any cell of a shared memory in unit time thus the issue of interprocessor communication do not get intermixed with the logical structure of parallel algorithms the paper is organized into four major sections section 2 deals with tree traversals there are three main algorithms that differ completely from one another in approach in absolute terms however all require a specific input form or designed to preprocess the input in desired form section 3 presents parallel algorithms for breadth first search of general graphs there are two major techniques for developing efficient parallel algorithms for breadth first search of a graph one is based on computation of shortest paths in a uniformly positive edge weighted graph the other is based on tree merging technique section 4 is devoted to parallel algorithms for depth first search of graphs considering the importance of depth first search as a general paradigm for algorithmic solution of several graph problem there have been lot of efforts to design efficient parallel algorithms for depth first search but the success so far has been restricted to small classes of graphs like directed acyclic graphs dag or planar graphs for dags there are two different techniques to obtain depth first spanning trees or forests viz lexicographic sorting of paths and tree merging in the case of the planar graph the technique is to recursively divide the input graph into smaller graphs by path separators and then run the algorithm in parallel on smaller graphs produced by the separators section 5 talks about car decomposition search of graphs and efficient parallel algorithms for the problem in fact ear decomposition search is considered as an alternative to depth first search in designing parallel algorithms for complicated graph problems the strategy used for car decomposition of a graph is almost identical to that used for orientation of the edges of a connected bridgeless undirected graph so that the resultant graph is strongly connected

improving space efficiency with path length prediction for finding k shortest simple paths finding mbi k shortest simple paths in a directed graph is a fundamental problem in many engineering applications most existing algorithms such as yen s algorithm and its variants have polynomial worst case time complexity but their average case running time is very high the heuristic algorithm mps can run significantly faster in practice however it requires an excessive amount of memory space in this paper we provide a new heuristic algorithm that achieves high space efficiency while maintaining similar average case running time we first propose a sidetrack representation of path with which a path can be stored in mbi o bf 1 space we then show how to categorize a candidate path as either partial or complete and restrict the number of paths added to the queue in addition we provide an empirical equation that can very accurately predict the mbi k th shortest path length provided that a much smaller number of shortest paths have been found extensive experiments prove that our algorithm can achieve an mbi o n speedup in practice over yen s algorithm in comparison with mps it runs up to three times faster and uses less space by an order of magnitude

a shortest augmenting path algorithm for the semi assignment problem the objective of this study is to develop a shortest augmenting path algorithm for solving the semi assignment problem and conduct an extensive computational comparison with the best alternative approaches the algorithm maintains dual feasibility and complementary slackness and works toward satisfying primal feasibility effective heuristics arc used to achieve an excellent advanced start and convergence is assured via the use of the shortest augmenting path procedure using reduced costs for arc lengths unlike other algorithms such as the primal simplex or the auction algorithm each iteration during the final phase of the procedure also known as the end game achieves one additional assignment the software implementations of our algorithm are fastest for the semi assignment problems that we tested our dense code is also faster than the best software for assignment problems in addition the algorithm has the best polynomial worst case running time bound that we have seen and the memory requirements are relatively small

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

personalized pagerank clustering a graph clustering algorithm based on random walks abstract graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications in addition exponential growth of real world graphs such as social networks biological networks and electrical circuits demands clustering algorithms with nearly linear time and space complexity in this paper we propose personalized pagerank clustering ppc that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph we combine random walks and modularity to precisely and efficiently reveal the clusters of a graph ppc is a top down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly linear approaches that are mainly bottom up it also gives a hierarchy of clusters that is useful in many applications ppc has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets furthermore its top down approach makes it a flexible solution for clustering problems with different requirements

a weighted kt t free t factor algorithm for bipartite graphs for a simple bipartite graph and an integer t 2 we consider the problem of finding a minimum weight kt t free t factor which is a t factor containing no complete bipartite graph kt t as a subgraph when t 2 this problem amounts to the square free 2 factor problem in a bipartite graph for the unweighted square free 2 factor problem a combinatorial algorithm is given by hartvigsen and the weighted version of the problem is np hard for general t pap designed a combinatorial algorithm for the unweighted version and makai gave a dual integral description of kt t free t matchings for a certain case where the weight vector is vertex induced on any subgraph isomorphic to kt t for this class of weight vectors we propose a strongly polynomial algorithm to find a minimum weight kt t free t factor the algorithm adapts the unweighted algorithms of hartvigsen and pap and a primal dual approach to the minimum cost flow problem the algorithm is fully combinatorial and thus provides a dual integrality theorem which is tantamount to makai s one

simulation relations for pattern matching in directed graphs we consider the problem of finding the occurrences of a pattern tree t in a directed graph g and propose two algorithms one for preprocessing and one for searching for t in g it is assumed that

fast approximate graph partitioning algorithms we study graph partitioning problems on graphs with edge capacities and vertex weights the problems of b balanced cuts and k balanced partitions are unified into a new problem called minimum capacity rho separators a rho separator is a subset of edges whose removal partitions the vertex set into connected components such that the sum of the vertex weights in each component is at most rho times the weight of the graph we present a new and simple o log n approximation algorithm for minimum capacity rho separators which is based on spreading metrics yielding an o log n approximation algorithm both for b balanced cuts and k balanced partitions in particular this result improves the previous best known approximation factor for k balanced partitions in undirected graphs by a factor of o log k we enhance these results by presenting a version of the algorithm that obtains an o log opt approximation factor the algorithm is based on a technique called spreading metrics that enables us to formulate directly the minimum capacity rho separator problem as an integer program we also introduce a generalization called the simultaneous separator problem where the goal is to find a minimum capacity subset of edges that separates a given collection of subsets simultaneously we extend our results to directed graphs for values of rho geq 1 2 we conclude with an efficient algorithm for computing an optimal spreading metric for rho separators this yields more efficient algorithms for computing b balanced cuts than were previously known

fsi analysis of liquid filled pipes most reported work on transient fluid structure interaction fsi in liquid filled pipes has been carried out in the time domain when needed information in the frequency domain e g frequency responses has been deduced by discrete fourier transforms in this paper the analysis is undertaken directly in the frequency domain and has the advantage of enabling linear dispersive terms to be included in a fully coupled manner in principle time domain results e g pressure histories can be obtained by numerical inverse laplace transforms in both domains the mathematical model has one pair of equations for each mode of wave propagation e g pressure waves in the liquid flexural waves in the pipe axial fsi coupling exists in the equations and also in boundary conditions the development used herein highlights common features between analysis in the frequency domain and analysis by the method of characteristics moc in the time domain a general formulation not restricted to pipe systems is presented the method is validated by comparison with an alternative exact analytical solution with results obtained by discrete fourier transform from an moc analysis and by comparison with measured data from a laboratory apparatus

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

the wave equation on asymptotically de sitter like spaces in this paper we obtain the asymptotic behavior of solutions of the klein gordon equation on lorentzian manifolds x g which are de sitter like at infinity such manifolds are lorentzian analogues of the so called riemannian conformally compact or asymptotically hyperbolic spaces under global assumptions on the null bicharacteristic flow namely that the boundary of the compactification x is a union of two disjoint manifolds y and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to and to the other manifold as the parameter goes to we also define the scattering operator and show that it is a fourier integral operator associated to the bicharacteristic flow from y to y

towards optimal parallel bucket sorting we present a simple deterministic parallel algorithm that runs on a crcw pram and sorts n integers of size polynomial in n in time o log n using o n log log nlog n processors it is closer to optimality than any previously known deterministic algorithm that solves the stated restricted sorting problem in polylog time

efficient implementation of graph algorithms using contraction the component merging problem is a new graph problem versions of this problem appear as bottlenecks in various graph algorithms a new data structure solves this problem efficiently and two special cases of the problem have even more efficient solutions based on other data structures the performance of the data structures is sped up by introducing a new algorithmic tool called packets the algorithms that use these solutions to the component merging problem also exploit new properties of two existing data structures specifically trees can be used simultaneously as a priority queue and a concatenable queue similarly f heaps support some kinds of split operations with no loss of efficiency an immediate application of the solution to the simplest version of the merging problem is an o t m n algorithm for finding minimum spanning trees in undirected graphs without using f heaps where t m n m log 2 log 2 log d n the graph has n vertices and m edges and d max m n 2 packets also improve the f heap minimum spanning tree algorithm giving the fastest algorithm currently known for this problem the efficient solutions to the merging problem and the new observation about f heaps lead to an o n t m n n log n algorithm for finding a maximum weighted matching in general graphs this settles an open problem posed by tarjan 15 p 123 where the weaker bound of o nm log n 2 m was conjectured

time version of the shortest path problem in a stochastic flow network many studies on hardware framework and routing policy are devoted to reducing the transmission time for a flow network a time version of the shortest path problem thus arises to find a quickest path which sends a given amount of data from the unique source to the unique sink with minimum transmission time more specifically the capacity of each arc in the flow network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc should be stochastic due to failure maintenance etc such a network is named a stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent under the time constraint t such a probability is named the system reliability in particular the data are transmitted through two minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all d t mps and the system reliability can then be computed in terms of d t mps moreover the optimal pair of minimal paths with highest system reliability could be obtained

time work tradeoffs for parallel algorithms some parallel algorithms have the property that as they are allowed to take more time the total work that they do is reduced this paper describes several algorithms with this property these algorithms solve important problems on directed graphs including breadth first search topological sort strong connectivity and and the single source shorest path problem all of the algorithms run on the erew pram model of parallel computer except the algorithm for strong connectivity which runs on the probabilistic erew pram

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

all pairs shortest paths in o n 2 time with high probability we present an all pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from 0 1 is o n2 in expectation and with high probability this resolves a long standing open problem the algorithm is a variant of the dynamic all pairs shortest paths algorithm of demetrescu and italiano 2006 the analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is o n2 in expectation and with high probability we also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in o log2n expected time

efficient approximation algorithms for bandwidth consecutive multicolorings of graphs let g be a graph in which each vertex v has a positive integer weight b v and each edge v w has a nonnegative integer weight b v w a bandwidth consecutive multicoloring simply called a b coloring of g assigns each vertex v a specified number b v of consecutive positive integers as colors of v so that for each edge v w all integers assigned to vertex v differ from all integers assigned to vertex w by more than b v w the maximum integer assigned to vertices is called the span of the coloring the b coloring problem asks to find a b coloring of a given graph g with the minimum span in the paper we present four efficient approximation algorithms for the problem which have theoretical performance guarantees for the computation time the span of a found b coloring and the approximation ratio we also obtain several upper bounds on the minimum span expressed in terms of the maximum b degrees one of which is an extension of brooks theorem on an ordinary coloring

future stability of the einstein non linear scalar field system we consider the question of future global non linear stability in the case of einstein s equations coupled to a non linear scalar field the class of potentials v to which our results apply is defined by the conditions v 0 0 v 0 0 and v 0 0 thus einstein s equations with a positive cosmological constant represents a special case obtained by demanding that the scalar field be zero in that context there are stability results due to helmut friedrich the methods of which are however not so easy to adapt to the presence of matter the goal of the present paper is to develop methods that are more easily adaptable due to the extreme nature of the causal structure in models of this type it is possible to prove a stability result which only makes local assumptions concerning the initial data and yields global conclusions in time to be more specific we make assumptions in a set of the form b 4r 0 p for some r 0 0 on the initial hypersurface and obtain the conclusion that all causal geodesics in the maximal globally hyperbolic development that start in b r 0 p are future complete furthermore we derive expansions for the unknowns in a set that contains the future of b r 0 p the advantage of such a result is that it can be applied regardless of the global topology of the initial hypersurface as an application we prove future global non linear stability of a large class of spatially locally homogeneous spacetimes with compact spatial topology

simple fast parallel hashing by oblivious execution a hash table is a representation of a set in a linear size data structure that supports constant time membership queries we show how to construct a hash table for any given set of n keys in o lg lg n parallel time with high probability using n processors on a weak version of a concurrent read concurrent write parallel random access machine crcw pram our algorithm uses a novel approach of hashing by oblivious execution based on probabilistic analysis the algorithm is simple and has the following structure partition the input set into buckets by a random polynomial of constant degree for t 1 to o lg lg n do allocate mt memory blocks each of size kt let each bucket select a block at random and try to injectively map its keys into the block using a random linear function buckets that fail carry on to the next iteration the crux of the algorithm is a careful a priori selection of the parameters mt and kt the algorithm uses only o lg lg n random words and can be implemented in a work efficient manner

technical note a note on parametric analysis in linear assignment a classic application of the linear assignment problem is the assignment of people to jobs or jobs to people in this context it is interesting to measure competition for jobs and to generate a suitable list of jobs from which a person can choose the length of the list is a parameter a known list generation procedure is based on an interior point method followed by a parametric analysis we describe a more efficient procedure exploiting linear assignment theory and shortest path computations further we propose an alternative list generation procedure based on a special type of dual values for the linear assignment problem

self adjusting heaps in this paper we explore two themes in data structure design amortized computational complexity and self adjustment we are motivated by the following observations in most applications of data structures we wish to perform not just a single operation but a sequence of operations possibly having correlated behavior by averaging the running time per operation over a worst case sequence of operations we can sometimes obtain an overall time bound much smaller than the worst case time per operation multiplied by the number of operations we call this kind of averaging amortization standard kinds of data structures such as the many varieties of balanced trees are specifically designed so that the worst case time per operation is small such efficiency is achieved by imposing an explicit structural constraint that must be maintained during updates at a cost of both running time and storage space however if amortized running time is the complexity measure of interest we can guarantee efficiency withou

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs

a parametrix for the fundamental solution of the klein gordon equation on asymptotically de sitter spaces abstract in this paper we construct a parametrix for the forward fundamental solution of the wave and klein gordon equations on asymptotically de sitter spaces without caustics we use this parametrix to obtain asymptotic expansions for solutions of u f and to obtain a uniform l p estimate for a family of bump functions traveling to infinity

vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method abstract branched pipes of arbitrary shapes are prevalent in pipe systems considering fluid structure interaction fsi an absorbing transfer matrix method in frequency domain for fluid filled pipelines with any branched pipes is proposed in this paper a dominant chain of pipeline would be selected and the point transfer matrix of each junction on the dominant chain would be determined here the point transfer matrix representing the influence of branched pipes at the junction on the dominant pipeline was absorbed by the dominant chain based on these with transfer matrixes of other elements the fluid and structure dynamics problem could be solved following the chain transfer matrix method process several numerical examples with different constraints are presented to illustrate the application of the proposed method moreover the experiment of cross shaped pipes with various boundary conditions was carried out and results from the present approach were validated by measured and numerical data then the forced vibrations of branched pipes were analyzed by considering the effects of various parameters which shows the fluid pressure and vibrations can be optimized by changing the branch angles and positions through these examples it is shown that the proposed method is efficient and can be used to calculate branched pipes of any shape

on t dependent hyperbolic systems part 2 abstract we consider hyperbolic equations with time dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times we are dealing with generic situations where the large time asymptotics is of hyperbolic type our approach is based on diagonalisation procedures combined with asymptotic integration arguments