the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

complexity of the discrete time cost tradeoff problem for project networks this note addresses the discrete version of the well known time cost tradeoff problem for project networks which has been studied previously in the standard project management literature as well as in the related literature on decision cpm all the algorithms proposed thus far for the solution of the general problem exhibit exponential worst case complexity with the notable exception of the pseudo polynomial dynamic program due to hindelang and muth we first demonstrate that this algorithm is flawed and that when we correct it it no longer remains pseudo polynomial continuing on in the main result of the note we show that this is not at all surprising since the problem is strongly np hard finally we discuss the complexities of various network structures and validate an old conjecture that certain structures are necessarily more difficult to solve

on stein neighborhood basis of real surfaces in this paper we show that a compact real surface embedded in a complex surface has a regular stein neighborhood basis provided that there are only finitely many complex points on the surface and that they are all flat and hyperbolic an application to unions of totally real planes in 2 is then given

analyticity on rotation invariant families of curves let be a rotation invariant family of smooth jordan curves contained in a the open unit disc in c for each t let dt be the simply connected domain bounded by t we present various conditions which imply that if is a continuous function on a such that for every fe the function f t has a continuous extension to dt which is analytic in dr then is analytic in a

a dual ascent approach for steiner tree problems on a directed graph the steiner tree problem on a directed graph stdg is to find a directed subtree that connects a root node to every node in a designated node setv we give a dual ascent procedure for obtaining lower bounds to the optimal solution value the ascent information is also used in a heuristic procedure for obtaining feasible solutions to the stdg computational results indicate that the two procedures are very effective in solving a class of stdg s containing up to 60 nodes and 240 directed 120 undirected arcs

analyticity on translates of a jordan curve let be a domain in which is symmetric with respect to the real axis and whose boundary is a real analytic simple closed curve translate vertically to get where is such that we prove that if is a continuous function on such that for each the function has a continuous extension to which is holomorphic on then is holomorphic on

a general approach to classification problems abstract in the classification problem the value of the discrete random variable i must be estimated from that of a random variable x given a random sample i1 x1 i2 x2 in xn a classification rule giving such an estimate can be based on most nonparametric density estimators which are based on delta sequences the rate at which the nonerror rate for this rule converges to the optimal is calculated it is found to be o n 1 2d 2 log d n where d is the dimension of the variable x under mild assumptions on the densities a procedure for choosing an associated parameter for small samples is given

a factoring approach for the steiner tree problem in undirected networks in communication networks many applications such as video on demand and video conferencing must establish a communications tree that spans a subset k in a vertex set the source node can then send identical data to all nodes in set k along this tree this kind of communication is known as multicast communication a network optimization problem called the steiner tree problem stp is presented to find a least cost multicasting tree in this paper an o e algorithm is presented to find a minimum steiner tree for series parallel graphs where e is the number of edges based on this algorithm we proposed an o 2 2 c e algorithm to solve the steiner tree problem for general graphs where c is the number of applied factoring procedures the c value is strongly related to the topology of a given graph this is quite different from other algorithms with exponential time complexities in k

lower bound for the mean project completion time in dynamic pert networks we apply the stochastic dynamic programming to obtain a lower bound for the mean project completion time in a pert network where the activity durations are exponentially distributed random variables moreover these random variables are non static in that the distributions themselves vary according to some randomness in society like strike or inflation this social randomness is modelled as a function of a separate continuous time markov process over the time horizon the results are verified by simulation

developing a heuristic algorithm for order production planning using network models under uncertainty conditions in this paper a practical and appropriate algorithm is provided for order production planning under uncertainty conditions producing the order production projects using different methodologies is facing uncertainty and therefore specific techniques are required to determine their production planning schedule network models combining fuzzy logic to define the sequence of the production stages and uncertainty are appropriate tools for order production planning modeling in this paper start time parameters of each activity duration of each activity and number of loops in the products production network are defined as triangular fuzzy numbers pessimistic possible optimistic and results of the production planning are defined as fuzzy sets in this paper network calculations including fuzzy forward cpm are performed output of this algorithm is a fuzzy order production schedule this method is more practical than existing production planning schedules determination methods and has less calculation and has upgrade and mechanization capability

a dual ascent procedure for large scale uncapacitated network design the fixed charge network design problem arises in a variety of problem contexts including transportation communication and production scheduling we develop a family of dual ascent algorithms for this problem this approach generalizes known ascent procedures for solving shortest path plant location steiner network and directed spanning tree problems our computational results for several classes of test problems with up to 500 integer and 1 98 million continuous variables and constraints show that the dual ascent procedure and an associated drop add heuristic generate solutions that in almost all cases are guaranteed to be within 1 to 4 of optimality moreover the procedure requires no more than 150 seconds on an ibm 3083 computer the test problems correspond to dense and sparse networks including some models that arise in freight transport

a dual ascent approach to the fixed charge capacitated network design problem abstract in this paper we consider the problem of constructing a network over which a number of commodities are to be transported fixed costs are associated to the construction of network arcs and variable costs are associated to routing of commodities in addition one capacity constraint is related to each arc the problem is to determine a network design that minimizes the total cost i e it balances the construction and operating costs a dual ascent procedure for finding improved lower bounds and near optimal solutions for the fixed charge capacitated network design problem is proposed the method is shown to generate tighter lower bounds than the linear programming relaxation of the problem

incremental modular decomposition modular decomposition is a form of graph decomposition that has been discovered independently by researchers in graph theory game theory network theory and other areas this paper reduces the time needed to find the modular decomposition of a graph from o n 3 to o n 2 together with a new algorithm for transitive orientation given in 21 this leads to fast new algorithms for a number of problems in graph recognition and isomorphism including recognition of comparability graphs and permutation graphs the new algorithm works by inserting each vertex successively into the decomposition tree using o n time to insert each vertex

estimation of a multivariate density function using delta sequences this paper studies some asymptotic properties of density estimates hat f of f based on d variate delta sequences the mean square consistency almost sure consistency and asymptotic normality of hat f have been obtained as corollaries to the l 1 convergence properties of these delta sequences estimators based on kernel functions orthogonal series and some histogram methods can be obtained as special cases of hat f

complexity results for the linear time cost tradeoff problem with multiple milestones and completely ordered jobs abstract we consider two linear project time cost tradeoff problems with multiple milestones unless a milestone is completed on time penalty costs for tardiness may be imposed however these penalty costs can be avoided by compressing the processing times of certain jobs that require additional resources or costs our model describes these penalty costs as the total weighted number of tardy milestone the first problem tries to minimize the total weighted number of tardy milestones within the budget for total compression costs while the second problem tries to minimize the total weighted number of tardy milestones plus total compression costs we develop a linear programming formulation for the case with a fixed number of milestones for the case with an arbitrary number of milestones we show that under completely ordered jobs the first problem is np hard in the ordinary sense while the second problem is polynomially solvable

a solution procedure for the discrete time cost and quality tradeoff problem using electromagnetic scatter search abstract decisions concerning a project s expedition traditionally involved considerations regarding time and cost tradeoff it was recently suggested that the quality of a project should also be taken into considerations in this paper we propose a meta heuristic solution procedure for the discrete time cost and quality tradeoff problem this problem involves the scheduling of project activities in order to minimize the total cost of the project while maximizing the quality of the project and also meeting a given deadline we apply a so called electromagnetic scatter search to solve this problem in this process we initially generate a population of feasible solutions in so doing we use frequency memory to well sample the feasible region a number of these solutions are then selected and improved locally the improved solutions are then combined to generate new set of solutions the combination process utilizes attraction repulsion mechanisms borrowed from the electromagnetism theory the whole process is stopped when no significant improvement in the set of solutions are observed the validity of the proposed solution procedure is demonstrated and its applicability is tested on a randomly generated large and complex problem having 19 900 activities

asymptotic efficiency of classifying procedures using the hermite series estimate of multivariate probability densities corresp pattern recognition procedures derived from a nonparametric estimate of multivariate probability density functions using the orthogonal hermite system are examined for sufficiently regular densities the convergence rate of the mean integrated square error mise is o n l epsilon epsilon 0 where n is the number of observations and is independent of the dimension as a consequence the rate at which the probability of misclassification converges to the bayes probability of error as the length n of the learning sequence tends to infinity is also independent of the dimension of the class densities and equals o n 1 2 delta delta o

polynomially convex hulls of singular real manifolds we obtain local and global results on polynomially convex hulls of lagrangian and totally real submanifolds of c n with self intersections and open whitney umbrella points

the recognition of series parallel digraphs we present a linear time algorithm to recognize the class of vertex series parallel vsp digraphs our method is based on the relationship between vsp digraphs and the class of edge series paralle

automatic pattern recognition a study of the probability of error a test sequence is used to select the best rule from a class of discrimination rules defined in terms of the training sequence the vapnik chervonenkis and related inequalities are used to obtain distribution free bounds on the difference between the probability of error of the selected rule and the probability of error of the best rule in the given class the bounds are used to prove the consistency and asymptotic optimality for several popular classes including linear discriminators nearest neighbor rules kernel based rules histogram rules binary tree classifiers and fourier series classifiers in particular the method can be used to choose the smoothing parameter in kernel based rules to choose k in the k nearest neighbor rule and to choose between parametric and nonparametric rules

on holomorphic extensions from spheres in ℂ2 a theorem of rudin states that if b is the open unit ball in n n 1 if 0 if is the family of all complex lines in n at a distance from the origin and if f c b is such that for every the function f b has a continuous extension to b which is holomorphic in b then f has a continuous extension to b which is holomorphic in b in this paper we show that when n 2 the theorem still holds if is replaced by a considerably smaller family

on the use of the complexity index as a measure of complexity in activity networks abstract a large number of optimal and suboptimal procedures have been developed for solving combinatorial problems modeled as activity networks the need to differentiate between easy and hard problem instances and the interest in isolating the fundamental factors that determine the computing effort required by these procedures inspired a number of researchers to develop various complexity measures in this paper we investigate the relation between the hardness of a problem instance and the topological structure of its underlying network as measured by the complexity index we demonstrate through a series of experiments that the complexity index defined as the minimum number of node reductions necessary to transform a general activity network to a series parallel network plays an important role in predicting the computing effort needed to solve easy and hard instances of the multiple resource constrained project scheduling problem and the discrete time cost trade off problem

a classification procedure using the multiple fourier series abstract a nonparametric procedure using the multiple fourier series is presented and examined conditions for the weak and strong bayes risk consistency are given and the rates at which the probability of misclassification converges to the bayes probability of error are presented the rates for the convergence in mean as well as w p 1 are independent of the dimension

parametric argument principle and its applications to cr functions and manifolds it follows from the classical argument principle that if a holomor phic mapping f from the unit discto c or more generally to c n smooth in the closed disc is homologicaly trivial on the unit circle i e h1 0 f s 1 which is equivalent to either being a point or having endpoints i e 6 then f const in other words the image of the unit disc degenerates to a point we establish a parametric version of this fact for a variety of holomorphic map pings fromto c n in place of a single mapping we find conditions for a holomorphic mapping of the unit disc depending on additional real parameters under which homological triviality of the boundary image implies collapse of the dimension of the image of the interior as an application we obtain estimates of dimensions of complex tan gent bundles of real submanifolds in c n in terms of zero moment conditions on families of closed curves covering the manifold apply ing this result to the graphs of functions we obtain solution of several known problems about characterization of holomorphic cr functions in terms of moment conditions on families of curves

on a paper by christofides et al for solving the multiple resource constrained single project scheduling problem abstract in a recently published article in ejor christofides et al cat present a depth first search branch and bound solution procedure for the multiple resource constrained single project scheduling problem while there are many important contributions in this paper we show by counterexample that if the branching strategy described by the authors is used the optimal solution might not result computational experience on a set of test problems appearing in the open literature is reported both with the original branching strategy suggested by the authors and a modified branching strategy that we propose the modified strategy guarantees the determination of the optimal solution in all instances of the problem at the expense of an increase in node evaluations and average cpu time computational results using the revised procedure and a hybrid breadth first search procedure also investigated by cat are reported

nonparametric estimation via empirical risk minimization a general notion of universal consistency of nonparametric estimators is introduced that applies to regression estimation conditional median estimation curve fitting pattern recognition and learning concepts general methods for proving consistency of estimators based on minimizing the empirical error are shown in particular distribution free almost sure consistency of neural network estimates and generalized linear estimators is established

approximation algorithms for the discrete time cost tradeoff problem due to its obvious practical relevance the time cost tradeoff problem has attracted the attention of many researchers over the last forty years while the linear time cost tradeoff problem can be solved in polynomial time its discrete variant is known to be np hard we present the first approximation algorithms for the discrete time cost tradeoff problem specifically given a fixed budget we consider the problem of finding a shortest schedule for a project we give an approximation algorithm with performance ratio 3 2 for the class of projects where all feasible durations of activities are either 0 1 or 2 we extend our result by giving approximation algorithms with performance guarantee olog l where l is the ratio of the maximum duration of any activity to the minimum nonzero duration of any activity finally we discuss bicriteria approximation algorithms which compute schedules for a given deadline or budget such that both project duration and cost are within a constant factor of the duration and cost of an optimum schedule for the given deadline or budget

resource allocation via dynamic programming in activity networks abstract we investigate the application of dynamic programming to the problem of resource allocation in a project with the objective of minimizing the project completion time we assume that there is a relationship between the amount of the resource allocated to an activity and its duration which is monotone nonincreasing in its argument the motivation for this study is the recent development of a procedure which yields the minimum number of nodes to be reduced in the an this drastically alters the complexity of the dp approach from o u h to o u c where h is the number of common activities and c is the minimum number of reduced nodes since typically h c we present and illustrate the dp optimizing procedure which is easily seen to be still plagued by the curse of dimensionality despite the drastic reduction in complexity mentioned above we then present an elementary approximating procedure which provides an upper bound on the optimum and is computationally more economical for c 3 we illustrate both procedures by a small numerical example continuing research is devoted to evaluating the efficacy of the approximating procedure and investigating other approximations

bounding the project completion time distribution in pert networks we consider the pert model of a project composed of activities whose durations are random variables with known distributions for the situations in which the activity durations are completely independent we present a new method for obtaining a probability distribution function that bounds the exact probability distribution of the project completion time from below the bounding distribution can be used to obtain an upper bound on the mean completion time of the project we also prove and illustrate that this bounding distribution is better tighter than any of the existing lower bounds implying that the corresponding upper bound on the mean completion time is tighter than any of the existing upper bounds

a random activity network generator exact and heuristic procedures are often developed to obtain optimal and near optimal solutions to decision problems modeled as activity networks testing the accuracy and efficiency of these procedures requires the use of activity networks with various sizes structures and parameters the size of the network is determined by its number of nodes and arcs where the structure is chosen from the set of all structures for the specified network size the network parameters depend on the nature of the decision problem often it is desirable for test problems to be generated at random from the space of all feasible networks this paper deals with the problem of generating the size and structure of the network at random from the space of all feasible networks it develops a theory which guarantees the randomness of the network structure the theory is the basis for two methods one can be used to generate dense networks where the other is used to generate nondense networks the methods which are practical a

holomorphic extensions from open families of circles for a circle z c z c p write z w z a w a 2 0 z a p a continuous function f on extends holomorphically from into the disc bounded by if and only if the function f z z f z defined on z z z e r has a bounded holomorphic extension into a r in the paper we consider open connected families of circles c write u u e c and assume that a continuous function on u extends holomorphically from each e c we show that this happens if and only if the function f z z f z defined on z z z e u has a bounded holomorphic extension into the domain u r e q for each open family q compactly contained in c this allows us to use known facts from several complex variables in particular we use the edge of the wedge theorem to prove a theorem on real analyticity of such functions

models and algorithms for network reduction abstract we study models and algorithms for a network reduction nr problem that entails constructing a reduced network in place of an existing large network so that the shortest path lengths between specified node pairs in this network are equal to or only slightly longer than the corresponding shortest path lengths in the original network solving this problem can be very useful both to accelerate shortest path calculations in many practical contexts and to reduce the size of optimization models that contain embedded shortest path problems this work was motivated by a real problem of scheduling and routing resources to perform spatially dispersed jobs but also has other applications we consider two variants of the nr problem a min size nr problem that minimizes the number of arcs in the reduced network while ensuring that the shortest path lengths in this network are close to the original lengths and a min length nr problem that minimizes a weighted sum of shortest path lengths over all the specified node pairs while limiting the number of arcs in the reduced network we model both problems as integer programs with multi commodity flows and propose optimization based heuristic algorithms to solve them these methods include preprocessing a shortest path based procedure with local improvement and a dual ascent algorithm we report on the successful applications to reduce the network for practical infrastructure project planning and to condense a transportation network for distribution planning we also compare these solutions with those obtained using algorithms for minimum length trees

a note on polynomial convexity of the union of finitely many totally real planes in c2 abstract in this paper we discuss local polynomial convexity at the origin of the union of finitely many totally real planes through 0 c 2 the planes say p 0 p n satisfy a mild transversality condition that enables us to view them in weinstock s normal form i e p 0 r 2 and p j m a j a j i i r 2 j 1 n where each a j is a 2 2 matrix with real entries weinstock has solved the problem completely for pairs of transverse maximally totally real subspaces in c n n 2 using a characterization of simultaneous triangularizability of 2 2 matrices over the reals given by florentino we deduce a sufficient condition for local polynomial convexity of the union of the above planes at 0 c 2 weinstock s theorem for c 2 occurs as a special case of our result

railroad blocking a network design application in this study we formulate the railroad blocking problems as a network design problem with maximum degree and flow constraints on the nodes and propose a heuristic lagrangian relaxation approach to solve the problem the newapproach decomposes the complicated mixed integer programming problem into two simple subproblems so that the storage requirement and computational effort are greatly reduced a set of inequalities are added to one subproblem to tighten the lower bounds and facilitate generating feasible solutions subgradient optimization is used to solve the lagrangian dual an advanced dual feasible solution is generated to speed up the convergence of the subgradient method the model is tested on blocking problems from a major railroad and the results show that the blocking plans generated have the potential to reduce the railroad s operating costs by millions of dollars annually

the exact overall time distribution of a project with uncertain task durations abstract this paper presents a new technique for computing the exact overall duration of a project when task durations have independent distributions a project is represented as an activity on arc aoa graph where a task begins as soon as all its predecessor tasks have finished task durations use a probability density function p d f which combines piecewise polynomial segments and dirac delta functions defined over a finite interval a semi analytical procedure is proposed to compute the cumulative distribution function c d f directly by integrating a linear transformation of the p d f of the task durations graph reduction techniques by hopcroft and tarjan and by valdes allow the problem to be broken into a series of smaller subproblems improving computational efficiency examples are presented to illustrate the proposed method

a note on a dual ascent approach to the fixed charge capacitated network design problem abstract we show by a counterexample that the dual ascent procedure proposed by herrmann ioannou minis and proth in a 1996 issue of the european journal of operational research is incorrect in the sense that it does not generate a valid lower bound to the optimal value of fixed charge capacitated network design problems we provide a correct dual ascent procedure based on the same ideas and we give an interpretation of it in terms of a simple lagrangean relaxation although correct this procedure is not effective as in general it provides a less tighter bound than the linear programming relaxation

improved algorithms for joint optimization of facility locations and network connections abstract this paper studies a k median steiner forest problem that jointly optimizes the opening of at most k facility locations and their connections to the client locations so that each client is connected by a path to an open facility with the total connection cost minimized the problem has wide applications in the telecommunication and transportation industries but is strongly np hard in the literature only a 2 approximation algorithm is known it being based on a lagrangian relaxation of the problem and using a sophisticated primal dual schema in this study we have developed an improved approximation algorithm using a simple transformation from an optimal solution of a minimum spanning tree problem compared with the existing 2 approximation algorithm our new algorithm not only achieves a better approximation ratio that is easier to be proved but also guarantees to produce solutions of equal or better quality up to 50 percent improvement in some cases in addition for two non trivial special cases where either every location contains a client or all the locations are in a tree shaped network we have developed for the first time in the literature new algorithms that can solve the problem to optimality in polynomial time

optimizing splitter and fiber location in a multilevel optical ftth network due to the emergence of bandwidth requiring services telecommunication operators are being compelled to renew their fix access network most of them favoring the fiber to the home ftth technology this paper focuses on the optimization of ftth deployment which is of prime importance due to the economic stakes the key design issue here is locating splitters and routing fi bers in an existing network infrastructure to which is associated a graph with given capacities on the edges no assumption is made on the structure of the graph first we propose a mixed integer formulation for this decision problem then valid inequalities and problem size reduction schemes are presented finally efficiency of solving approaches is assessed through extensive numerical tests performed on orange real life data

threshold based preprocessing for approximating the weighted dense k subgraph problem abstract based on an application in forestry we study the dense k subgraph problem given a parameter k n and an undirected weighted graph g the task is to find a subgraph of g with k vertices such that the sum of the weights of the induced edges is maximized the problem is well known to be np hard and difficult to approximate if the underlying graph does not satisfy the triangle inequality in the present paper we develop a fast preprocessing routine which results in a graph still containing a 1 1 k approximation for the problem the key idea is to identify vertices which are of low interest to an optimal solution for the problem due to falling below a special threshold using this information we initiate a chain reaction of vertex eliminations to reduce the number of vertices in the input graph without losing a lot of information this graph reduction step runs in polynomial time the success of this preprocessing step mainly depends on finding a large threshold which ensures that many vertices can be removed for this purpose we devise an efficient algorithm which yields a provably optimal threshold finally we present empiric studies for our application even though the graphs tied to our application in forestry have several hundred vertices and do not satisfy the triangle inequality they exhibit special properties which yield a very favorable performance of our approach the pruning step typically removes more than 90 of the vertices and thus enables an optimal solution of the problem on the reduced graph

optimal reduction of two terminal directed acyclic graphs algorithms for series parallel graphs can be extended to arbitrary two terminal dags if node reductions are used along with series and parallel reductions a node reduction contracts a vertex with unit in degree out degree into its sole incoming outgoing neighbor this paper gives an o n 2 5 algorithm for minimizing node reductions based on vertex cover in a transitive auxiliary graph applications include the analysis of pert networks dynamic programming approaches to network problems and network reliability for np hard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices this gives improvements if the underlying graph is nearly series parallel

bin packing with controllable item sizes we consider a natural resource allocation problem in which we are given a set of items where each item has a list of pairs associated with it each pair is a configuration of an allowed size for this item together with a nonnegative penalty and an item can be packed using any configuration in its list the goal is to select a configuration for each item so that the number of unit bins needed to pack the sizes plus the sum of penalties is minimized this problem has applications in operating systems bandwidth allocation and discrete time cost tradeoff planning problems for the offline version of the problem we design an augmented asymptotic ptas that is an asymptotic approximation scheme that uses bins of size slightly larger than 1 we further consider the online bounded space variant where only a constant number of bins can be open simultaneously we design a sequence of algorithms where the sequence of their competitive ratios tends to the best possible asymptotic competitive ratio finally we study the bin covering problem in which a bin is covered if the sum of sizes allocated to it is at least 1 in this setting penalties are interpreted as profits and the goal is to maximize the sum of profits plus the number of covered bins we design an algorithm of best possible competitive ratio which is 2 we generalize our results for online algorithms and unit sized bins to the case of variable sized bins where there may be several distinct sizes of bins available for packing or covering and get that the competitive ratios are again the same as for the more standard online problems

a graph theoretic game and its application to the k server problem this paper investigates a zero sum game played on a weighted connected graph g between two players the tree player and the edge player at each play the tree player chooses a spanning tree t and the edge player chooses an edge e the payoff to the edge player is cost t e defined as follows if e lies in the tree t then cost t e 0 if e does not lie in the tree then cost t e cycle t e w e where w e is the weight of edge e and cycle t e is the weight of the unique cycle formed when edge e is added to the tree t the main result is that the value of the game on any n vertex graph is bounded above by exp o sqrt log n log log n it is conjectured that the value of the game is o log n the game arises in connection with the k server problem on a road network i e a metric space that can be represented as a multigraph g in which each edge e represents a road of length w e it is shown that if the value of the game on g is val g w then there is a randomized strategy that achieves a competitive ratio of k 1 val g w against any oblivious adversary thus on any n vertex road network there is a randomized algorithm for the k server problem that is k cdot exp o sqrt log n log log n competitive against oblivious adversaries at the heart of the analysis of the game is an algorithm that provides an approximate solution for the simple network design problem specifically for any n vertex weighted connected multigraph the algorithm constructs a spanning tree t such that the average over all edges e of cost t e is less than or equal to exp o sqrt log n log log n this result has potential application to the design of communication networks it also improves substantially known estimates concerning the existence of a sparse basis for the cycle space of a graph

a fast algorithm for the decomposition of graphs and posets many combinatorial optimization problems of graphs e g finding maximal independent sets or maximum matchings and acyclic networks e g finding shortest paths or maximum flows can be solved by means of decomposition of the graph network into autonomous subsets given a relation r on a a subset b of a is called autonomous if for each a b the following holds if 0 r for some 0 b then r for all b if 0 r for some 0 b then r for all b we present an algorithm which finds all autonomous subsets of graphs and posets with p points in o p3 time and o p2 space the ideas behind this algorithm reveal rather strong connections between graph decomposition homomorphisms of graphs and posets and comparability graph recognition furthermore the well known series parallel decomposition for graphs and posets is contained as a special case

propagation of boundary cr foliations and morera type theorems for manifolds with attached analytic discs abstract we prove that homologically nontrivial generic smooth 2 n 1 parameter families of analytic discs in c n n 2 attached by their boundaries to a cr manifold test cr functions in the following sense if a smooth function on analytically extends into any analytic discs from the family then the function satisfies tangential cr equations on in particular we give an answer theorem 1 to the following long standing open question so called strip problem earlier solved only for special families mainly for circles given a smooth one parameter family of jordan curves in the plane and a function f admitting holomorphic extension inside each curve must f be holomorphic on the union of the curves we prove for real analytic functions and arbitrary generic real analytic families of curves that the answer is yes if no point is surrounded by all curves from the family the latter condition is essential we generalize this result to characterization of complex curves in c 2 as real 2 manifolds admitting nontrivial families of attached analytic discs theorem 4 the main result implies fairly general morera type characterization of cr functions on hypersurfaces in c 2 in terms of holomorphic extensions into three parameter families of attached analytic discs theorem 2 one of the applications is confirming in real analytic category the globevnik stout conjecture theorem 3 on boundary values of holomorphic functions it is proved that a smooth function on the boundary of a smooth strictly convex domain in c n extends holomorphically inside the domain if it extends holomorphically into complex lines tangent to a given strictly convex subdomain the proofs are based on a universal approach namely on the reduction to a problem of propagation from the boundary to the interior of degeneracy of cr foliations of solid torus type manifolds theorem 2 2

optimal rates of convergence to bayes risk in nonparametric discrimination consider the multiclassification discrimination problem with known prior probabilities and a multi dimensional vector of observations assume the underlying densities corresponding to the various classes are unknown but a training sample of size n is available from each class rates of convergence to bayes risk are investigated under smoothness conditions on the underlying densities of the type often seen in nonparametric density estimation these rates can be drastically affected by a small change in the prior probabilities so the error criterion used here is bayes risk averaged uniformly over all prior probabilities then it is shown that a certain rate n r is optimal in the sense that no rule can do better uniformly over the class of smooth densities and a rule is exhibited which does that well the optimal value of r depends on the smoothness of the distributions and the dimensionality of the observations in the same way as for nonparametric density estimation with integrated square error loss

testing analyticity on rotation invariant families of curves let r c c be a piecewise smooth jordan curve symmetric with respect to the real axis which contains the origin in its interior and which is not a circle centered at the origin let q be the annulus obtained by rotating r around the origin we characterize the curves r with the property that if f e c q is analytic on sr for every 181 1 then f is analytic in int q

zero integrals on circles and characterizations of harmonic and analytic functions we determine the kernels of two circular radon transforms of continuous functions on an annulus and use this to obtain a characterization of harmonic functions in the open unit disc which involves poisson averages over circles computed at only one point of the disc and to obtain a version of morera s theorem which involves only the circles which surround the origin

beyond the markovian assumption response excitation probabilistic solution to random nonlinear differential equations in the long time uncertainty quantification for dynamical systems under non white excitation is a difficult problem encountered across many scientific and engineering disciplines difficulties originate from the la