linear time algorithm to cover and hit a set of line segments optimally by two axis parallel squares abstract this paper discusses the problem of covering and hitting a set of line segments l in r 2 by a pair of axis parallel congruent squares of minimum size we also discuss the restricted version of covering where each line segment in l is to be covered completely by at least one square the proposed algorithms assume that the input segments are given in a read only array for each of these problems i e covering hitting and restricted covering problems our proposed algorithm reports the optimum result by executing only two passes of reading the input array sequentially all these algorithms need only o 1 extra space the solution of these problems also give a 2 approximation for covering and hitting those line segments l by two congruent disks of minimum radius with same computational complexity

on anstreicher s combined phase i phase ii projective algorithm for linear programming anstreicher has proposed a variant of karmarkar s projective algorithm that handles standard form linear programming problems nicely we suggest modifications to his method that we suspect will lead to better search directions and a more useful algorithm much of the analysis depends on a two constraint linear programming problem that is a relaxation of the scaled original problem

fuzzy versions of the covering circle problem abstract in this paper we consider two fuzzy versions of the well known problem of determining the smallest circle center and radius that would cover a given finite set of points in the plane when the locations of points are not precise but fuzzy the first is modeled as a possibility constrained mathematical program while the second is modeled as a necessity constrained one polynomial algorithms are presented for both the versions also a numerical example is included for one case these models and solutions are of interest in both theoretical and practical contexts

brief linear mpc with optimal prioritized infeasibility handling application computational issues and stability all practical mpc implementations should have a means to recover from infeasibility we present a recently developed infeasibility handler which computes optimal relaxations of the relaxable constraints subject to a user defined prioritization by solving only a single linear program on line in addition to the standard quadratic programming problem on line a stability result for this infeasibility handler combined with the rawlings muske mpc controller is provided and various practical and computational issues are discussed from a simulated fccu main fractionator case study we conclude that the proposed strategy for designing the proposed infeasibility handler is applicable to the problems of realistic size

a randomized algorithm for fixed dimensional linear programming we give a las vegas randomized algorithm for linear programming in a fixed dimensiond for which the expected computation time is o d 3 varepsilon d d n where limd e d 0 this improves the corresponding worst case complexity o 3 d 2 n the method is based on a recent idea of clarkson two variations on the algorithm are examined briefly

low dimensional linear programming with violations two decades ago megiddo and dyer showed that linear programming lp in two and three dimensions and subsequently any constant number of dimensions can be solved in linear time in this paper we consider the lp problem with at most k violations i e finding a point inside all but at most k halfspaces given a set of n halfspaces we present a simple algorithm in two dimensions that runs in o n k2 log n expected time this is faster than earlier algorithms by everett robert and van kreveld 1993 and matousek 1994 for many values of k and is probably near optimal an extension of our algorithm in three dimensions runs in near o n k11 4n1 4 expected time interestingly the idea is based on concave chain decompositions or covers of the le k level previously used in proving combinatorial k level bounds applications in the plane include improved algorithms for finding a line that misclassifies the fewest among a set of bichromatic points and finding the smallest circle enclosing all but k points we also discuss related problems of finding local minima in levels

in search of an optimal dilution algorithm for feedforward networks in a recent paper the authors presented a dilution algorithm that yields a storage capacity per synapse alpha eff larger than 2 in this letter two new algorithms with even higher alpha eff values are introduced they study a one step dilution algorithm where the perceptron is used to select a fraction of the couplings to be removed for the remaining bonds the perceptron of optimal stability is relearned they further compare simulation data from an iterative version of the one step dilution algorithm with phase space volume calculations

projection based polygonality measurement measuring the degree to which a shape resembles a polygon referred to as polygonality is a difficult problem due to the intrinsic diversity in the form and distortion of shapes caused by digitization and similarity transformation this paper proposes a generic approach for this problem by performing the measurement in the projection space where the radon image of some primitive shapes which compose the shape becomes apparent the obtained measures take value in 0 1 with 1 corresponding to analytical polygons they are robust to additive noise and boundary distortion and is invariant to similarity transformation the new framework generalizes existing polygonal measures such as triangularity and quadrangularity in addition the ability to estimate polygon s geometric quantities in the projection space allows approximating a shape by analytical polygons the efficiency of the proposed approach is demonstrated through a number of experiments on both synthetic and real data sets

a geometrical solution for quadratic bicriteria location models this paper deals with a single facility unweighted quadratic bicriteria location problem defined in the continuous space first we describe an analytical method for constructing the set of pareto optimal locations for this problem based on the farthest point voronoi diagram then we present an analytical method for finding the solution to the scalarized location problems based on the pareto optimal locations the analytical results enable planners to carry out some sensitivity analyses since both methods are based entirely on geometrical analysis they can be understood intuitively

out of roundness problem revisited the properties and computation of the minimum radial separation mrs standard for out of roundness are discussed another standard out of roundness measurement called the minimum area difference mad center is introduced although the two centers have different characteristics the approach to finding both centers shares many commonalities an o n log n k time algorithm which is used to compute the mrs center is presented it also computes the mad center of a simple polygon g where n is the number of vertices of g and k is the number of intersection points of the medial axis and the farthest neighbor voronoi diagram of g the relationship between mrs and mad is discussed

on stability of multiobjective nmpc with objective prioritization this paper proposes a new multiobjective model predictive control mo mpc of constrained nonlinear systems according to objective prioritization the mo mpc problem is formulated as a lexicographic optimization problem the optimal solutions are obtained by solving a hierarchy of single objective optimization problems the conditions guaranteeing the recursive feasibility of the optimization problem and stability of the closed loop system are derived which depend only on the most important objective moreover a suboptimal algorithm is presented to reduce the computational demand of mo mpc one characteristic of the proposed mo mpc is that the given objective prioritization is automatically satisfied the theoretical results are illustrated by a comparison study of an example

stabilizing model predictive control of hybrid systems in this note we investigate the stability of hybrid systems in closed loop with model predictive controllers mpc a priori sufficient conditions for lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion while allowing for discontinuous system dynamics and discontinuous mpc value functions for constrained piecewise affine pwa systems as prediction models we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions for quadratic mpc costs these conditions translate into a linear matrix inequality while for mpc costs based on 1 infin norms they are obtained as norm inequalities new ways for calculating low complexity piecewise polyhedral positively invariant sets for pwa systems are also presented an example illustrates the developed theory

the discrete and mixed minimax 2 center problems abstract letting p be a set of n points in the plane the discrete minimax 2 center problem d m m 2 c p is to find two disks centered at p 1 p 2 p that minimize the maximum of two terms namely the euclidean distance between two centers and the distance of any other point to the closer center the mixed minimax 2 center problem m m m 2 c p is when one of the two centers is not in p we present algorithms solving the d m m 2 c p and m m m 2 c p the time complexities of solving the d m m 2 c p and m m m 2 c p are o n 2 log n and o n 2 log 2 n respectively furthermore we consider two steiner minimum sum dipolar spanning tree problems in which one of the two dipoles is a steiner point and the dipoles are both steiner points these two problems are shown to be solvable in o n log n and o n time respectively

on the generalization ability of diluted perceptrons a linearly separable boolean function is teamed by a diluted perceptron with optimal stability a different level of dilution is allowed for teacher and student perceptron the learning algorithms used were the optimal annealed dilution and hebbian dilution the generalization ability i e the probability to recognize a pattern which has not been learned before is calculated in replica symmetry

efficiency of characterizing ellipses and ellipsoids by discrete moments in this paper our studies are focused on ellipses and problems related to their representation and reconstruction from the data resulting from their digitization the main result of the paper is that a finite number of discrete moments corresponded to digital ellipses is in one to one correspondence with digital ellipses which enables coding of digital ellipses with an asymptotically optimal amount of memory in addition the problem of reconstruction based on the same parameters is considered since the digitization of real shapes causes an inherent loss of information about the original objects the precision of the original shape estimation from the corresponding digital data is limited we derive a sharp upper bound for the errors in reconstruction of the center position and half axes of the ellipse in function of the applied picture resolution i e the number of pixels per unit an extension of these results to the 3d case is also given

a dynamic data structure for 3 d convex hulls and 2 d nearest neighbor queries we present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions where insertions take o log3n expected amortized time deletions take o log6n expected amortized time and extreme point queries take o log2n worst case time this is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions and improves the previous o ne time method by agarwal and matousek a decade ago as a consequence we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems such as levels in three dimensions and dynamic euclidean minimum spanning trees in the plane

linear time algorithms for linear programming in r 3 and related problems linear time algorithms for linear programming in r 2 and r 3 are presented the methods used are applicable for other graphic and geometric problems as well as quadratic programming for exam

perceptrons above saturation we study the storage of random patterns by a perceptron above its storage capacity alpha c i e in the region where perfect storage becomes impossible we determine the minimal fraction of learning errors and the distribution of stabilities for different learning rules in one step replica symmetry breaking thereby we not only extend the known replica symmetric results to values of the storage capacity beyond the at line but also show that depending on the learning rule replica symmetry may be globally unstable already well below the at line as an example for possible implications we compare the results for the typical basins of attraction of an extremely diluted attractor neural network as given by replica symmetry and one step replica symmetry breaking

a general framework to design stabilizing nonlinear model predictive controllers abstract we propose a new model predictive control mpc framework to generate feedback controls for time varying nonlinear systems with input constraints we provide a set of conditions on the design parameters that permits to verify a priori the stabilizing properties of the control strategies considered the supplied sufficient conditions for stability can also be used to analyse the stability of most previous mpc schemes the class of nonlinear systems addressed is significantly enlarged by removing the traditional assumptions on the continuity of the optimal controls and on the stabilizability of the linearized system some important classes of nonlinear systems including some nonholonomic systems can now be stabilized by mpc in addition we can exploit increased flexibility in the choice of design parameters to reduce the constraints of the optimal control problem and thereby reduce the computational effort in the optimization algorithms used to implement mpc

fuzzy disk for covering fuzzy points abstract in this paper we consider an important fuzzy version of the well known smallest covering circle problem which is also called the euclidean 1 center problem here we are given a set of points in the plane whose locations are crisp however the requirement for coverage of each point is fuzzy as represented by its grade of membership as such we qualify the points as fuzzy in the above framework we wish to find a fuzzy disk with minimum fuzzy area for covering the given fuzzy points after developing a general model certain special cases are investigated in detail polynomial algorithms are presented for the special cases

measure of circularity for parts of digital boundaries and its fast computation this paper focuses on the design of an effective method that computes the measure of circularity of a part of a digital boundary an existing circularity measure of a set of discrete points which is used in computational metrology is extended to the case of parts of digital boundaries from a single digital boundary two sets of points are extracted so that the circularity measure computed from these sets is representative of the circularity of the digital boundary therefore the computation consists of two steps first the inner and outer sets of points are extracted from the input part of a digital boundary using digital geometry tools next the circularity measure of these sets is computed using classical tools of computational geometry it is proved that the algorithm is linear in time in the case of convex parts thanks to the specificity of digital data and is in o nlogn otherwise experiments done on synthetic and real images illustrate the interest of the properties of the circularity measure

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

dynamic minimum bichromatic separating circle abstract in the minimum bichromatic separating circle problem given a set r of n red points and a set b of m blue points the goal is to find the smallest radius circle c that contains all red points and the smallest possible number of blue points in this paper we study the dynamic version of the problem which we call the dynamic minimum bichromatic separating circle problem and present data structures that allow to perform efficient reporting and updates under insertion and removal of blue points we first describe a unified linear size data structure that allows both insertions and deletions of blue points then we present a data structure that allows to report an optimal circle in o log m n time when only insertions of blue points are allowed at the expense of an increase in update time and storage finally we give a data structure that achieves o log 2 m n reporting time when only deletions of blue points are allowed with the same update time and storage as the insertions only data structure our results are the first known for the dynamic minimum bichromatic separating circle problem

digital convexity straightness and convex polygons new schemes for digitizing regions and arcs are introduced it is then shown that under these schemes sklansky s definition of digital convexity is equivalent to other definitions digital convex polygons of n vertices are defined and characterized in terms of geometric properties of digital line segments also a linear time algorithm is presented that given a digital convex region determines the smallest integer n such that the region is a digital convex n gon

brief paper improving performance in model predictive control switching cost functionals under average dwell time in this paper we propose a novel switched model predictive control mpc algorithm for nonlinear continuous time systems where we switch between different cost functionals in order to enhance performance thus different performance criteria can be taken into account in order to ensure stability of the resulting closed loop system we consider switching signals which exhibit a certain average dwell time when considering switching signals of this type certain assumptions are common in the switched systems literature in order to ensure stability like a matching condition for the different lyapunov functions and the possibility to find lyapunov functions with an exponential decay rate in this paper we show how these assumptions can be satisfied in the mpc context and thus stability of the proposed switched mpc algorithm can be established

algorithms for the robust 1 center problem on a tree abstract we consider the weighted 1 center problem on a network with uncertainty in node weights and edge lengths uncertainty is modelled by means of interval estimates for parameters specifically each uncertain parameter is assumed to be random with unknown distribution and can take on any value within a corresponding prespecified interval it is required to find a robust minmax regret solution that is a location which is e optimal for any possible realization of parameters with e as small as possible the problem on a general network is known to be np hard for the problem on a tree we present a polynomial algorithm

fuzzy facility location problem with preference of candidate sites models so far considered as facility location problems treat either min max or max min criterion that is the facility is either desirable or undesirable we propose the following model considering the satisfaction degree with respect to the distance from the facility for each customer residents and preference of the site in an urban area the objective is to find the site of the facility which maximizes the minimal satisfaction degree among all demand points and maximizes the preference of the site since generally speaking there exists no site that maximizes both criteria we seek non dominated sites after defining non domination

propositional logic in control and monitoring problems by using linear constraints on integer variables logical inference can be incorporated within model predictive control and model based detection problems resulting in mixed integer quadratic or mixed integer linear programming problems qualitative knowledge can be used to prioritize control objectives or to improve performance of detection schemes this article demonstrates some capabilities of combining logic using integer variables with quantitative models

separating point sets by circles and the recognition of digital disks given two sets a and b of points in the plane we give a polynomial time algorithm to find the set s of points which are centers of circles that contain all the members of a and none of b a consequence of the algorithm is that s is polygonal another application is an o n2 time and o n2 space algorithm for the recognition of digital disks

k center and k median problems in graded distances graded distances are generalizations of the euclidean distance on points in r1 they have been used in the study of special cases of np hard problems in this paper we study the k center and k median problems with graded distance matrices we first prove that the k center problem is polynomial time solvable when the distance matrix is graded up the rows or graded down the rows we then prove that the k median problem is np complete when the distance matrix is graded up the rows or graded down the rows an easy special case of the k median problem with graded distance matrices is also discussed

stability of multiobjective predictive control we propose a utopia tracking strategy to handle multiple conflicting objectives in model predictive control the controller minimizes the distance of its vector of objectives to that of the compromise solution the point along the steady state pareto front closest to the utopia point where all the objectives are independently minimized we establish conditions for asymptotic stability and propose numerical implementation variants one of the key advantages of the approach is that it avoids the computation of pareto fronts in real time environments in addition the approach can handle general objectives of different nature such as economic and regularization

on the complexity of the elzinga hearn algorithm for the 1 center problem we show that the complexity of the elzinga hearn algorithm for the 1 center single facility minimax problem is n2 we also show that the algorithm reaches a solution within any given accuracy in on time

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

optimal storage properties of neural network models the authors calculate the number p alpha n of random n bit patterns that an optimal neural network can store allowing a given fraction f of bit errors and with the condition that each right bit is stabilised by a local field at least equal to a parameter k for each value of alpha and k there is a minimum fraction fmin of wrong bits they find a critical line alpha c k with alpha c 0 2 the minimum fraction of wrong bits vanishes for alpha alpha c k the calculations are done using a saddle point method and the order parameters at the saddle point are assumed to be replica symmetric this solution is locally stable in a finite region of the k alpha plane including the line alpha c k but there is a line above which the solution becomes unstable and replica symmetry must be broken

learning algorithms with optimal stability in neural networks to ensure large basins of attraction in spin glass like neural networks of two state elements xi imu or 1 the authors propose to study learning rules with optimal stability delta where delta is the largest number satisfying delta or sigma j jij xi jmu xi imu mu 1 p i 1 n where n is the number of neurons and p is the number of patterns they motivate this proposal and provide optimal stability learning rules for two different choices of normalisation for the synaptic matrix jij in addition numerical work is presented which gives the value of the optimal stability for random uncorrelated patterns

the space of interactions in neural network models the typical fraction of the space of interactions between each pair of n ising spins which solve the problem of storing a given set of p random patterns as n bit spin configurations is considered the volume is calculated explicitly as a function of the storage ratio alpha p n of the value kappa 0 of the product of the spin and the magnetic field at each site and of the magnetisation m here m may vary between 0 no correlation and 1 completely correlated the capacity increases with the correlation between patterns from alpha 2 for correlated patterns with kappa 0 and tends to infinity as m tends to 1 the calculations use a saddle point method and the order parameters at the saddle point are assumed to be replica symmetric this solution is shown to be locally stable a local iterative learning algorithm for updating the interactions is given which will converge to a solution of given kappa provided such solutions exist

a deep cut ellipsoid algorithm for convex programming theory and applications this paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems in each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided moreover for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed finally some computational results of the deep and central cut version of the algorithm applied to a min max stochastic queue location problem are reported

multiobjective model predictive control this paper proposes a novel model predictive control mpc scheme based on multiobjective optimization at each sampling time the mpc control action is chosen among the set of pareto optimal solutions based on a time varying state dependent decision criterion compared to standard single objective mpc formulations such a criterion allows one to take into account several often irreconcilable control specifications such as high bandwidth closed loop promptness when the state vector is far away from the equilibrium and low bandwidth good noise rejection properties near the equilibrium after recasting the optimization problem associated with the multiobjective mpc controller as a multiparametric multiobjective linear or quadratic program we show that it is possible to compute each pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular pareto optimal solution furthermore we provide conditions for selecting pareto optimal solutions so that the mpc control loop is asymptotically stable and show the effectiveness of the approach in simulation examples

reconstruction of a digital circle abstract since digitization always causes some loss of information reconstruction of the original figure from a given digitization is a challenging task reconstruction of digital circles has already been addressed in the literature however an in depth analysis of an obq image of a continuous circle as well as a solution to its domain construction problem is still lacking in this paper a detailed analysis of digital circles has been carried out a modified i r method is formulated to numerically compute the domain of each digital quarter circle for a given radius several properties of the obq image of a circle reveal that in many cases it is possible to split a digital circle into four digital quarter circles such that the domains of the individual quarter circles can be combined to obtain the domain of the full circle moreover the domain of a quarter circle is geometrically characterized

the number of n point digital discs a digital disc is the set of all integer points inside some given disc let dn be the number of different digital discs consisting of n points different up to translation the upper bound d n o n2 was shown recently no corresponding lower bound is known in this paper we refine the upper bound to dn o n which seems to be the true order of magnitude and we show that the average dn d1 d2 dn n has upper and lower bounds which are of polynomial growth in n

structural properties of voronoi diagrams in facility location problems with continuous demand we consider facility location problems where the demand is continuously and uniformly distributed over a convex polygon with m vertices in the rectilinear plane n facilities are already present and the goal is to find an optimal location for an additional facility based on an analysis of structural properties of incremental voronoi diagrams we develop polynomial exact algorithms for five conditional location problems the developed methodology is applicable to a variety of other facility location problems with continuous demand moreover we briefly discuss the euclidean case

a dilution algorithm for neural networks a dilution algorithm to enlarge the storage capacity per synapse alpha eff of neural networks is proposed the algorithm is a hybrid method where hebb s rule is used to select a fraction of couplings to be removed afterwards the perceptron of optimal stability for the remaining couplings is learned the authors present an analytical calculation and the results of the numerical simulations in comparison with the fully connected or the randomly diluted perceptron the effective storage capacity alpha eff is remarkably enlarged

layered neural networks exact solutions for the dynamics of layered feedforward neural networks are presented these networks are expected to respond to an input by going through a sequence of preassigned states on the various layers the family of networks considered has a variety of interlayer couplings linear and non linear hebbian hebbian with gaussian synaptic noise and with various kinds of dilution in addition the authors also solve the problem of layered networks with the pseudoinverse projector matrix of couplings in all cases the solutions take the form of layer to layer recursions for the mean overlap with a random key pattern and for the width of the embedding field distribution the dynamics is governed by the fixed points of these recursions for all cases non trivial domains of attraction of the memory states are found and graphically displayed

efficient algorithms for center problems in cactus networks efficient algorithms for solving the center problems in weighted cactus networks are presented in particular we have proposed the following algorithms for the weighted cactus networks of size n an o nlogn time algorithm to solve the 1 center problem and an o nlog 3n time algorithm to solve the weighted continuous 2 center problem we have also provided improved solutions to the general p center problems in cactus networks the developed ideas are then applied to solve the obnoxious 1 center problem in weighted cactus networks

suboptimal model predictive control feasibility implies stability practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex nonlinear optimization problems are possible in limited computational time in the paper we first establish conditions under which suboptimal model predictive control mpc controllers are stabilizing the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost second we present and analyze two suboptimal mpc schemes that are guaranteed to be stabilizing provided an initial feasible solution is available and for which the computational requirements are more reasonable

from shrinking to percolation in an optimization model a model of noise reduction for signal processing and other optimization tasks is introduced each noise source puts a symmetric constraint on the space of the signal vector within a tolerance bound when the number of noise sources increases sequences of transitions take place causing the solution space to vanish we find that the transition from an extended solution space to a shrunk space is retarded because of the symmetry of the constraints in contrast with the analogous problem of pattern storage for low tolerance the solution space vanishes by volume reduction whereas for high tolerance the vanishing becomes more and more like percolation

minmax regret 1 facility location on uncertain path networks abstract let p be an undirected path graph of n vertices each edge of p has a positive length and a constant capacity every vertex has a nonnegative supply which is an unknown value but is known to be in a given interval the goal is to find a point on p to build a facility and move all vertex supplies to the facility such that the maximum regret is minimized the previous best algorithm solves the problem in o n log 2 n time and o n log n space in this paper we present an o n log n time and o n space algorithm and our approach is based on new observations and algorithmic techniques

an o n algorithm for the multiple choice knapsack linear program an algorithm for solving the linear program associated with the multiple choice knapsack problem is described the algorithm is shown to work in time linear in the number of variables this improves the previously known best bound for this problem and is optimal to within a constant factor

one dimensional k center on uncertain data problems on uncertain data have attracted significant attention due to the imprecise nature of many measurement data in this paper we consider the k center problem on one dimensional uncertain data the input is a set p of weighted uncertain points on a real line and each uncertain point is specified by its probability density function pdf which is a piecewise uniform function i e a histogram the goal is to find a set q of k points on the line to minimize the maximum expected distance from the uncertain points of p to their expected closest points in q we present efficient algorithms for this uncertain k center problem and their running times almost match those for the deterministic k center problem

algorithms for a minimum volume enclosing simplex in three dimensions we develop a combinatorial algorithm for determining a minimum volume simplex enclosing a set of points in cal r 3 if the convex hull of the points has n vertices then our algorithm takes theta n 4 time combining our exact but slow algorithm with a simple but crude approximation technique we also develop an varepsilon approximation algorithm the algorithm computes in o n 1 varepsilon 6 time a simplex whose volume is within 1 varepsilon factor of the optimal for any varepsilon 0

an efficient algorithm for the smallest enclosing ball problem in high dimensions abstract consider the problem of computing the smallest enclosing ball of a set of m balls in r n this problem arises in many applications such as location analysis military operations and pattern recognition etc in this paper we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max 0 t and then develop a simple algorithm particularly suitable for problems in high dimensions this algorithm could efficiently handle problems of dimension n up to 10 000 under a moderately large m as well as problems of dimension m up to 10 000 under a moderately large n numerical results are given to show the efficiency of algorithm

digitized circular arcs characterization and parameter estimation the digitization of a circular arc causes an inherent loss of geometrical information arcs with slightly different local curvature or position may lead to exactly the same digital pattern in this paper the authors give a characterization of all centers and radii of circular arcs yielding the same digitization pattern the radius of the arcs varies over the set however only one curvature or radius estimate can be assigned to the digital pattern the authors derive an optimal estimator and give expressions for the bound on the precision of estimation this bound due to digitization is the deterministic equivalent of the cramer rao bound known from parameter estimation theory consider the estimation of the local curvature and local radius of a smooth object typically such parameters are estimated by moving a window along the digital boundary methods in literature show a poor precision in estimating curvature values relative errors of over 40 are often found from the definition of curvature it follows that locally the curve can be considered a circular arc and hence the method presented in this paper can be applied to the pattern in the window giving estimates with optimal precision and a measure for the remaining error on the practical side the authors present examples of the residual error due to the discrete grid the estimation of the radius or curvature of a circular arc at random position with an estimation window containing 10 points coded with nine freemancodes has a relative deviation exceeding 2 for a full disk the deviation is below 1 when the radius r exceeds four grid units the presented method is particularly useful for problems where some prior knowledge on the distribution of radii is known and where there is a noise free sampling