vector quantization of speech and speech like waveforms an algorithm for the design of vector quantizers that are locally optimum in the sense of minimizing an average quantitative distortion measure is used to design 1 and 2 bit sample vector quantizers for both real sampled speech and a simulated speech like auto regressive random process both weighted and unweighted squared error distortion measures are considered several comparisons are made and discussed based on the average distortions of the vector quantization schemes the results for the simulated speech are compared to mathematical performance bounds from information theory to provide an indication of how nearly globally optimal vector quantization is for such highly correlated sources a comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and hence of the applicability of information theory bounds and code designs based on probabilistic models the signal to quantization noise ratios of vector quantizers designed to minimize squared error distortion are compared to those of several popular speech waveform coding systems of similar rates

vector quantizers with direct sum codebooks the use of direct sum codebooks to minimize the memory requirements of vector quantizers is investigated assuming arbitrary fixed partitions necessary conditions for minimum distortion codebooks are derived first for scalar codebooks assuming mean squared error distortion and then for vector codebooks and a broader class of distortion measures an iterative procedure is described for designing locally optimal direct sum codebooks both optimal and computationally efficient suboptimal encoding schemes are considered it is shown that although an optimal encoding can be implemented by a sequential encoder the complexity of implementing optimal stagewise partitions generally exceeds the complexity of an exhaustive search of the direct sum codebook it is also shown that sequential nearest neighbor encoders can be extremely inefficient the m search method is explored as one method of improving the effectiveness of suboptimal sequential encoders representative results for simulated direct sum quantizers are presented

a pyramid vector quantizer the geometric properties of a memoryless laplacian source are presented and used to establish a source coding theorem motivated by this geometric structure a pyramid vector quantizer pvq is developed for arbitrary vector dimension the pvq is based on the cubic lattice points that lie on the surface of an l dimensional pyramid and has simple encoding and decoding algorithms a product code version of the pvq is developed and generalized to apply to a variety of sources analytical expressions are derived for the pvq mean square error mse and simulation results are presented for pvq encoding of several memoryless sources for large rate and dimension pvq encoding of memoryless laplacian gamma and gaussian sources provides rose improvements of 5 64 8 40 and 2 39 db respectively over the corresponding optimum scalar quantizer although suboptimum in a rate distortion sense because the pvq can encode large dimensional vectors it offers significant reduction in rose distortion compared with the optimum lloyd max scalar quantizer and provides an attractive alternative to currently available vector quantizers

transfer matrix inverison identities for exactly solvable lattice spin models a new functional equation satisfied by the commuting row to row transfer matrices is derived for the eight vertex model functional equations of the same form are satisfied by hard hexagons magnetic hard squares the self dual potts models the andrews baxter forrester models and others these new functional equations are called inversion identities because they generalize the inversion relation for local transfer matrices it is conjectured that all solvable models satisfying yang baxter equations possess such inversion identities and that in general these functional equations can be solved for the transfer matrix eigenvalues

high resolution quantization theory and the vector quantizer advantage the authors consider how much performance advantage a fixed dimensional vector quantizer can gain over a scalar quantizer they collect several results from high resolution or asymptotic in rate quantization theory and use them to identify source and system characteristics that contribute to the vector quantizer advantage one well known advantage is due to improvement in the space filling properties of polytopes as the dimension increases others depend on the source s memory and marginal density shape the advantages are used to gain insight into product transform lattice predictive pyramid and universal quantizers although numerical prediction consistently overestimated gains in low rate 1 bit sample experiments the theoretical insights may be useful even at these rates

multiple source shortest paths in embedded graphs let g be a directed graph with n vertices and nonnegative weights in its directed edges embedded on a surface of genus g and let f be an arbitrary face of g we describe a randomized algorithm to preprocess the graph in o gn log n time with high probability so that the shortest path distance from any vertex on the boundary of f to any other vertex in g can be retrieved in o log n time our result directly generalizes the o n log n time algorithm of klein proceedings of the 16th annual acm siam symposium on discrete algorithms 2005 for multiple source shortest paths in planar graphs intuitively our preprocessing algorithm maintains a shortest path tree as its source point moves continuously around the boundary of f as an application of our algorithm we describe algorithms to compute a shortest noncontractible or nonseparating cycle in embedded undirected graphs in o g 2 n log n time with high probability our high probability time bounds hold in the worst case for g

a note on stability of the constant cost dynamic lot size model by k richter in a paper by k richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed in particular an algorithm is suggested to compute the stability region of a so called generalized solution in general this region is only a subregion of the stability region of the optimal solution in this note we show that in a computational effort that is of the same order as the running time of richter s algorithm it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution

hard squares with diagonal attractions the authors complete the solution of the square lattice gas with nearest neighbour exclusion and attractive next nearest neighbour diagonal interactions on the special surface corresponding to regimes iii and iv of the generalised hard hexagon model the interfacial tension correlation length and sublattice density difference are calculated throughout these regimes by obtaining the eigenvalues of the row to row and corner transfer matrices the associated critical exponents are found to be mu v 5 4 beta 3 32 in regime iii and mu v 5 2 beta 1 4 in regime iv in particular their results confirm the recent proposal by huse that regime iii is the first order coexistence surface separating the disordered fluid phase from the square ordered solid phases and that the regime iii regime iv boundary is a line of tricritical points

sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions sufficient conditions are presented for uniqueness of a locally optimal quantizer being a stationary point of the quantization distortion measure e f x eta the expected value of an error weighting function f x eta where x is a random variable to be quantized where the probability density function p x describing x is continuous and positive on some finite or infinite interval and zero outside it and where eta is the quantization error the function f x eta is assumed convex and symmetric in eta and zero only for eta 0 it is shown that in the cases of f x eta eta 2 and f x eta eta the simple condition of concavity of in p x is sufficient for uniqueness of a locally optimal quantizer

vector quantizer design for memoryless gaussian gamma and laplacian sources locally optimum vector quantizer vq designs are presented for memoryless gaussian gamma and laplacian sources for gaussian sources low 2 6 dimensional vector quantization provides relatively little improvement in mean squared error mse compared to the minimum mean squared error mmse scalar quantizer for laplacian or gamma sources however significant improvement in mse is available with vector quantization the laplacian and gamma 6 bit sixdimensional vector quantizers achieve respectively improvements of 2 and 4 5 db over the corresponding scalar mmse quantizer distortions

operator content of the multicritical magnetic hard square model the transfer matrix spectra of the magnetic hard squares along the multicritical line are analysed using the data for the strip width n up to 12 the operator content of the model is exactly the same as that of the ashkin teller model when n is odd the spectrum is accounted for by the continuum theory in which the antiperiodic boundary condition is imposed to one of the ising variables of the ashkin teller model

the complexity of the generalized lloyd max problem corresp a simple combinatorial special case of the generalized lloyd max or quantization problem is shown to be nondeterministic polynomial np complete em a fortiori the general problem of communication theory in its combinatorial forms has at least that complexity

trellis coded vector quantization trellis coded quantization is generalized to allow a vector reproduction alphabet three encoding structures are described several encoder design rules are presented and two design algorithms are developed it is shown that for a stationary ergodic vector source if the optimized trellis coded vector quantization reproduction process is jointly stationary and ergodic with the source then the quantization noise is zero mean and of a variance equal to the difference between the source variance and the variance of the reproduction sequence several examples illustrate the encoder design procedure and performance

lattice derivation of modular invariant partition functions on the torus the author expresses the partition functions of the ade lattice models on the torus in terms of partition function of six vertex models and which can be computed in the continuum limit thus the author recovers the partition function of minimal models with c 1 and new ones with c 1

optimum quantizer performance for a class of non gaussian memoryless sources the performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources for a general distortion criterion necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer under a mean square error criterion the performance of entropy encoded uniform quantization of memoryless gaussian sources is well known to be within 0 255 bits sample of the rate distortion bound at relatively high rates despite claims to the contrary it is demonstrated that similar performance can be expected for a wide range of memoryless sources indeed for the cases considered the worst case performance is observed to be less than 0 3 bits sample from the rate distortion bound and in most cases this disparity is less at iow rates

operator content of the ashkin teller quantum chain superconformal and zamolodchikov fateev invariance ii boundary conditions compatible with the torus for pt i see ibid vol 20 no 8 p l479 85 1987 the authors present the operator content of the ashkin teller quantum chain with eight boundary conditions corresponding to the eight elements of the group d4 which gives the global symmetry of the system this operator content is a conjecture based on an extensive numerical study and was proven to be correct at the ising decoupling point for the values of the coupling constant where n 2 superconformal invariance was seen for free boundary conditions the situation is now more complex one finds sectors which have n 2 and n 1 superconformal invariance and sectors which have no superconformal invariance at all if however they combine the wrong sectors of the spectra which correspond to two different values of the coupling constant a new symmetry shows up they also analyse the operator content at the fateev zamolodchikov points here the wrong sectors can be described by a few new primary fields

a vector quantizer for the laplace source the low complexity nearly optimal vector quantizer vq is a generalization of t r fischer s 1986 pyramid vq and is similar in structure to the unrestricted polar quantizers previously presented for the independent gaussian source an analysis of performance is presented with results for both the product code pyramid vq and the unrestricted version this analysis although asymptotic in nature helps to demonstrate the performance advantages of the vq implementation issues of the vq are discussed nonasymptotic results are considered in particular the author presents an approximate design algorithm for finite bit rate and demonstrates the usefulness of this vq through several example designs with monte carlo simulations of performance for the restricted form the pyramid vq the author provides further implementational information and low dimension analytical results

fast algorithms for bipartite network flow we discuss network flow in a bipartite graph g with node sets s and t we show that karzanov s algorithm runs in time o s 2 t on g and that the mpm algorithm can be modified to run in the same bound for the common case that the degree of each node in t is bounded by a constant we show that a modified version of the mpm algorithm runs in time o s 3 s t on g the importance of these results comes from the common occurrence of problems that can be modeled and solved using network flow on bipartite graphs where s ll t in many applications involving bounded degree on the nodes in t t theta s 2 and our results reduce the best bounds on bipartite flow from o s 6 to o s 3 we use our results on bipartite flow to obtain the fastest known bounds on several combinatorial problems and mention several additional problems involving bipartite flow where s is much smaller than t

inversion identities for the self dual potts and ashkin teller models the commuting diagonal to diagonal transfer matrices of the self dual potts and ashkin teller models on the square lattice are shown to satisfy special functional equations called inversion identities these identities generalise the known local inversion or unitarity relations for interaction round a face or irf models satisfying yang baxter or star triangle equations

robust quantization of memoryless sources using dispersive fir filters an approach to quantizing discrete time memoryless sources is presented an important feature is that its performance is largely insensitive to errors in modeling the input pdf the method involves changing the amplitude distribution of the source to be approximately gaussian by all pass filtering then applying a lloyd max quantizer designed for a gaussian source after quantization the samples are passed through another all pass filter which is an approximate inverse of the first filter the mean square error mse for the overall process is roughly equal to the quantization mse for the intermediate gaussian signal independent of the source statistics for some sources this is actually an improvement over direct correct model lloyd max quantization the cost of this technique is some delay due to filtering

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

geometric source coding and vector quantization a geometric formulation is presented for source coding and vector quantizer design motivated by the asymptotic equipartition principle the authors consider two broad classes of source codes and vector quantizers elliptical codes and quantizers based on the gaussian density function and pyramid codes and quantizers based on the laplacian density function elliptical and weighted pyramid vector quantizers are developed by selecting codewords as points in a lattice that lie on or near a specified ellipse or pyramid the combination of geometric structure and lattice basis allows simple encoding and decoding algorithms

branching rules for unitary representations of virasoro and super virasoro algebras at c 1 the branching rules for unitary highest weight representations of virasoro and super virasoro algebras that contain a subalgebra with central charge c 1 are presented these rules are useful for identifying points of higher symmetry in two dimensional critical systems with c 1 and for the analysis of a defected ising chain

boundary conditions and inversion indentities for solvable lattice models with a sublattice symmetry the transfer matrices of solvable lattice spin models are considered under general boundary conditions associated with the symmetry of the models it is shown how the full symmetry can be exploited for systems having a sublattice symmetry by considering an extended model where the states distinguish the sublattices in this extended scheme the parity of the number of sites is tied to the boundary conditions the inversion identities can be extended and be used to obtain the full operator content of the critical models as an application the complete spectra of the transfer matrices for the eight vertex model at the decoupling point are calculated

integrable and conformal twisted boundary conditions for sl 2 a d e lattice models we study integrable realizations of conformal twisted boundary conditions for s 2 unitary minimal models on a torus these conformal field theories are realized as the continuum scaling limit of critical g a d e lattice models with positive spectral parameter u 0a nd coxete rnumber g i ntegrable seams are constructed by fusing blocks of elementary local face weights the usual a type fusions are labelled by the kac labels r s and are associated with the ve rlinde fusion algebra we introduce a new type of fusion in the two braid limits u i associated with the graph fusion algebra and labelled by nodes a b g respectively when combined with automorphisms they lead to general integrable seams labelled by x r a b ag 2 h h z2 where h is the graph g for type i theories and its parent for type ii theories identifying our construction labels with the conformal labels of petkova and zuber we find that the integrable seams are in one to one correspondence with th ec onformal seams the distinct seams are thus associated with the nodes of the ocneanu quantum graph the quantum symmetries and twisted partition functions are checked numerically for g 6 we also show in the case of d2 t hat the non commutativity of the ocneanu algebra of seams arises because the automorphisms do not commute with the fusions

an algorithm for uniform vector quantizer design a vector quantizer maps a k dimensional vector into one of a finite set of output vectors or points although certain lattices have been shown to have desirable properties for vector quantization applications there are as yet no algorithms available in the quantization literature for building quantizers based on these lattices an algorithm for designing vector quantizers based on the root lattices a n d n and e n and their duals is presented also a coding scheme that has general applicability to all vector quantizers is presented a four dimensional uniform vector quantizer is used to encode laplacian and gamma distributed sources at entropy rates of one and two bits sample and is demonstrated to achieve performance that compares favorably with the rate distortion bound and other scalar and vector quantizers finally an application using uniform four and eight dimensional vector quantizers for encoding the discrete cosine transform coefficients of an image at 0 5 bit pel is presented which visibly illustrates the performance advantage of vector quantization over scalar quantization

scaling dimensions and conformal anomaly in anisotropic lattice spin models the effect of anisotropic interactions on the eigenvalue spectrum of the row to row transfer matrix of critical lattice spin models is investigated it is verified that the predictions of conformal theory apply to anisotropic systems if one allows for spatial rescaling by incorporating an anisotropy factor zeta ay ax sin theta where ay and ax are lattice spacings and theta is an angle describing the anisotropy for exactly solvable models these anisotropy angles can be calculated analytically using corner transfer matrices this is done for the eight vertex model hard hexagons and interacting hard squares and it is found that theta pi u lambda 10u 3 and 5u respectively where u is the spectral parameter and lambda is the crossing parameter for each of these models the amplitude of the finite size corrections to the free energy at criticality is found to be of the form pi zeta c 6n2 where zeta is the anisotropy factor and the central charge or conformal anomaly is given by c 1 4 5 and 7 10 respectively this is an analytic result for the eight vertex model for the hard hexagon and square models the largest eigenvalues are found accurately by numerically solving their inversion identities for various anisotropies and strip widths up to n 48 finally the authors argue that the anisotropy angle for magnetic hard squares and the q state potts models is also given by theta pi u lambda so this result is quite general

local state probabilities for an infinite sequence of solvable lattice models the authors present a new infinite sequence of solvable lattice models they contrast strikingly with the eight vertex solid on solid models and admit extra degrees of freedom for the local fluctuation variables the exact one point functions are obtained the result is neatly described in terms of theta function identities using their modular invariance critical behaviour is studied and exponents evaluated

multiple local optima in vector quantizers corresp two results are presented on vector quantizers meeting necessary conditions for optimality first a simple generalization of well known centroid and moment properties of the squared error distortion measure to a weighted quadratic distortion measure with an input dependent weighting is presented the second result is an application of the squared error special case of the first result to a simulation study of the design of 1 bit per sample two and three dimensional quantizers for a memoryless gaussian source using the generalized lloyd technique the existence of multiple distinct local optima is demonstrated thereby showing that sufficient conditions for unique local optima do not exist for this simple common case it is also shown that at least three dimensions are required for a vector quantizer to outperform a scalar quantizer for this source

the root lattices as low bit rate vector quantizers vector quantizers based on the a and d lattices are explored using the mean square error mse fidelity criterion for independent identically distributed sources with normal laplacian and gamma probability density functions code books are studied for uniform coding rates of up to 2 b sample and two and four dimensions the expected mse performance of the quantizers is better than that of optimal nonuniform lloyd max quantizers while the design algorithm presented offers only modest improvements in mse performance for a normally distributed source improvement gains of up to several decibels can be achieved when coding laplacian and gamma sources

an efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection given an undirected graph g v e with v n and e m nonnegative integers ce and de for each edge e in e and a bound d the constrained minimum spanning tree problem cst is to find a spanning tree t v et such that sum e in e t d e leq d and sum e in e t c e is minimized we present an efficient polynomial time approximation scheme eptas for this problem specifically for every epsilon 0 we present a 1 epsilon approximation algorithm with time complexity o frac 1 epsilon o frac 1 epsilon n 4 our method is based on lagrangian relaxation and matroid intersection

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

exact solubility of the dn series the author shows that the dn series of a newly constructed set of models is completely integrable in particular the model described by d4 is a non critical extension of the three state self dual potts model

the economic lot sizing problem with an emission capacity constraint abstract we consider a generalisation of the lot sizing problem that includes an emission capacity constraint besides the usual financial costs there are emissions associated with production keeping inventory and setting up the production process because the capacity constraint on the emissions can be seen as a constraint on an alternative objective function there is also a clear link with bi objective optimisation we show that lot sizing with an emission capacity constraint is np hard and propose several solution methods our algorithms are not only able to handle a fixed plus linear cost structure but also more general concave cost and emission functions first we present a lagrangian heuristic to provide a feasible solution and lower bound for the problem for costs and emissions such that the zero inventory property is satisfied we give a pseudo polynomial algorithm which can also be used to identify the complete set of pareto optimal solutions of the bi objective lot sizing problem furthermore we present a fully polynomial time approximation scheme fptas for such costs and emissions and extend it to deal with general costs and emissions special attention is paid to an efficient implementation with an improved rounding technique to reduce the a posteriori gap and a combination of the fptases and a heuristic lower bound extensive computational tests show that the lagrangian heuristic gives solutions that are very close to the optimum moreover the fptases have a much better performance in terms of their actual gap than the a priori imposed performance and especially if the heuristic s lower bound is used they are very fast

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

fractional covers for forests and matchings we give polynomial algorithms for the fractional covering problems for forests andb matchings min 1 y ya w y 0 wherea is a matrix whose rows are the incidence vectors of forests b matchings respectively it is shown that each problem can be solved by a series of max flow min cut calculations and hence the use of the ellipsoid algorithm to guarantee a polynomial algorithm can be avoided

dn models local densities the author computes the local densities of the dn series whose integrability was shown in a previous letter see ibid vol 20 no 4 p l217 20 1987

the hexagon theorem we wish to int s z f z 2 s the unit square over all choices of f z which take just n values for large n it is shown that f z approaches that function which on each face of a hexagonal mesh has the value of the centroid of that face this problem in the design of quantizers for a pulse code modulation pcm system arose in which pairs of adjacent samples are quantized in an effort to capitalize on the correlation between samples and on the geometry of the plane

an algorithm for the multiparametric 0 1 integer linear programming problem relative to the objective function abstract the multiparametric 0 1 integer linear programming 0 1 ilp problem relative to the objective function is a family of 0 1 ilp problems in which the problems are related by having identical constraint matrix and right hand side vector in this paper we present an algorithm to perform a complete multiparametric analysis

continuously varying exponents in magnetic hard squares the commuting row to row transfer matrices of magnetic hard squares on the multicritical t manifold are shown to satisfy a special functional equation called an inversion identity for strip widths up to n 32 these equations are solved numerically for the transfer matrix eigenvalues the central charge or conformal anomaly c 1 is obtained from 1 n2 corrections to the exact bulk free energy and scaling dimensions are obtained from the eigenvalue gaps the magnetic scaling dimension is xm 1 8 and the sublattice density difference scaling dimension is xe 1 9 2 y where y 2 lambda pi and the interaction dependent crossing parameter lambda varies between 0 and 2 pi 3 scaling dimensions for further operators fall in the sequence xn n2xe where n 1 2 3 4 the critical exponents also vary continuously along the multicritical line and are given by alpha 14 9y 16 9y beta m 9 2 y 16 16 9y beta e 1 2 16 9y nu 9 2 y 2 16 9y and delta 15 these exponents are simply related to the exponents of the critical eight vertex and ashkin teller models which also exhibit z2 z2 symmetry and the authors argue that these models lie in the same universality class

an algorithm for the design of generalized quantizers for detection a procedure based on the generalized lloyd algorithm approach using a sequence of independent noise samples to design m region generalized quantizers for signal detection is presented included in this case are the conventional m interval quantizer detectors the quantizer parameters for s a kassam s 1985 four region generalized quantizer detector are computed using various sample sizes for the known sequence of independent noise samples two families of densities which cover a wide spectrum of possible nongaussian densities are considered the generalized gaussian densities and the johnson s sub u family of densities the performance of the quantizer detector is compared to that of the locally optimum detector and the results are presented as the asymptotic relative efficiencies of the respective detectors the case when the noise density is not known before analysis is considered and the detection performance is examined using an estimate of the density a mean squared error distortion criterion is used in the proposed algorithm to obtain quantizers that yield maximum efficacy it is shown through numerical examples that the design procedure is simple fast and applicable to a wide range of nongaussian distributions

parametric module allocation on partial k trees the problem of allocating modules to processors in a distributed system to minimize total costs when the underlying communication graph is a partial k tree and all costs are linear functions of a real parameter t is considered it is shown that if the number of processors is fixed the sequence of optimum assignments that are obtained as t varies from zero to infinity can be constructed in polynomial time as an auxiliary result a linear time separator algorithm for k trees is developed the implications of the results for parametric versions of the weighted vertex cover independent set and 0 1 quadratic programming problems on partial k trees are discussed

uniform spherical coordinate quantization of spherically symmetric sources for signal quantization with the minimum mean square error criterion optimum spherical coordinate quantizers have been shown to outperform optimum rectangular coordinate qnantizers for many spherically symmetric sources in this paper spherical coordinate quantizers are designed and analyzed under the added constraint that each scalar quantizer is a uniform equal step size quantizer it is shown that for small block length uniform spherical coordinate quantizers outperform the uniform rectangular coordinate quantizer as well as the uniform qnantizer consisting of a tesselation of the minimum inertia space filling polytope

parametric combinatorial computing and a problem of program module distribution en calcul parametrique certaines parties de la description du probleme sont donnees comme des fonctions d un ou plusieurs parametres pouvant varier sur un grand nombre de valeurs des valeurs fixes des parametres specifient un probleme particulier l objectif du calcul parametrique etant de resoudre de maniere efficace de tels problemes en fonction des valeurs des parametres on propose une methode de calcul parametrique generale efficace pour une large classe de problemes combinatoires la methode est liee a une methode developpee par megiddo pour la resolution de problemes d optimisation de ratios on traite un exemple de distribution de modules de programme d ordinateur entre deux processeurs

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

a parametric maximum flow algorithm for bipartite graphs with applications abstract suppose we are given a capacitated bipartite network g with node sets s and t in network g the arc capacities are not fixed values but are functions of a single parameter where is a continuous real variable our problem is to determine the minimum value of such that the maximum flow value in the corresponding network equals a given threshold for this problem an algorithm of time complexity o nm 2 log m n is presented where n is the number of nodes in s m is the number of nodes in t and n m examples are then given to show how to use this parametric algorithm to solve practical problems

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding

asymptotic performance of unrestricted polar quantizers corresp unrestricted polar quantizers upq s were previously introduced to overcome the weak mean squared error performance of polar coordinate quantizers for the independent bivariate gaussian source when the number of levels was small bits dimension an asymptotic ntean squared error analysis of the upq s with a general circularly symmetric source is presented the performance of the upq s is shown to be asymptotically within 0 17 db of that of the optimum bivariate quantizer the results are extended to dimensions greater than two examples for the independent gaussian source are included

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result