a new benes network control algorithm a new benes network control algorithm is presented unlike the original looping algorithm the new algorithm is not recursive in this algorithm n x n benes network is viewed as a concatenation of two subnetworks sn1 and sn2 the first log n 1 stages of a benes network correspond to sn1 and the remaining log n stages correspond to sn2 sn1 is controlled by a full binary tree of set partitioning functions called a complete residue partition tree and sn2 is bit controlled the new control algorithm sets switches one stage at a time stage by stage

on a class of rearrangeable networks benes networks are nonblocking rearrangeable networks that can realize arbitrary permutations without conflict a class of 2 log sub b n stage networks which are equivalent to the benes networks is introduced networks in this class can be either symmetric or asymmetric in their structure regular or irregular in their interstage connections and even 2 log sub b n or 2 log sub b n 1 stages all networks in this class are nonblocking rearrangeable a switch labeling scheme is proposed to provide testing of the topological and functional equivalency for this class of networks this switch labeling scheme can also provide a novel matrix representation for network configuration this representation introduces a portability concept for the routing scheme on this class of networks with this representation a general routing scheme is also developed this routing scheme can realize arbitrary permutation for the whole class of 2 log sub b n stage networks

markov chain algorithms for planar lattice structures consider the following markov chain whose states are all domino tilings of a 2n 2n chessboard starting from some arbitrary tiling pick a 2 2 window uniformly at random if the four squares appearing in this window are covered by two parallel dominoes rotate the dominoes 90 rm o in place repeat many times this process is used in practice to generate a random tiling and is a widely used tool in the study of the combinatorics of tilings and the behavior of dimer systems in statistical physics analogous markov chains are used to randomly generate other structures on various two dimensional lattices this paper presents techniques which prove for the first time that in many interesting cases a small number of random moves suffice to obtain a uniform distribution

on tiling under tomographic constraints given a tiling of a 2d grid with several types of tiles we can count for every row and column how many tiles of each type it intersects these numbers are called the projections we are interested in the problem of reconstructing a tiling which has given projections some simple variants of this problem involving tiles that are 1 1 or 1 2 rectangles have been studied in the past and were proved to be either solvable in polynomial time or np complete in this note we make progress toward a comprehensive classification of various tiling reconstruction problems by proving np completeness results for several sets of tiles

parallel permutation and sorting algorithms and a new generalized connection network o k log n algorithms are obtained to permute and sort n data items on cube and perfect shuffle computers with n sup 1 1 k processing elements 1 k log n these algorithms lead directly to a generalized connection network construction having o k log n delay and o kn sup 1 1 k log n contact pairs this network has the advantage that the switches can be set in o k log n time by either a cube or perfect shuffle computer with n sup 1 1 k processing elements 23 references

minimal multicut and maximal integer multiflow a survey we present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems such as the multiterminal cut and the unsplittable flow problems we consider neither continuous multiflow nor minimum cost multiflow most of the results are very recent and some are new we recall the dual relationship between both problems give complexity results and algorithms firstly in unrestricted graphs and secondly in several special graphs trees bipartite or planar graphs a table summarizes the most important results

the kr benes network a control optimal rearrangeable permutation network the benes network has been used as a rearrangeable network for over 40 years yet the uniform n 2 log n 1 control complexity of the n spl times n benes is not optimal for many permutations in this paper we present a novel o log n depth rearrangeable network called kr benes that is permutation specific control optimal the kr benes routes every permutation with the minimal control complexity specific to that permutation and its worst case complexity for arbitrary permutations is bounded by the benes thus it replaces the benes when considering control complexity latency we design the kr benes by first constructing a restricted 2log k 2 depth rearrangeable network called k benes for routing k bounded permutations with control 2n log k 0 spl les k spl les n 4 we then show that the n spl times n benes network itself with one additional stage contains every kr benes network as a subgraph and use this property to construct the kr benes network with regard to the control optimality of the kr benes we show that any optimal network for rearrangeably routing k bounded permutations must have depth 2log k 2 and therefore the k benes and hence the kr benes is optimal

analysis of aperiodicities in nearly periodic waveforms waveforms from the oscillations of sustained tone acoustic musical instruments are never precisely periodic the source of their aperiodicity is instrument dependent and typically small with the exception of some studies on the period fluctuations of bowed string instruments musical instrument aperiodicities have never been quantitatively characterized this paper introduces two techniques for the characterization of nearly periodic waveforms the norm difference method and the fourier transform of sonograms the former is appropriate for the study of cycle to cycle fluctuations and yields its best results for fluctuations that have a typical time scale of up to 16 periods of the nominally periodic oscillation the second method is appropriate for a frequency range of 2 hz to approximately 100 hz the ranges of applicability overlap for pitch frequencies in the treble region the techniques are described in detail and explored with various computer constructed waveforms with appropriate properties de

reconstruction of 4 and 8 connected convex discrete sets from row and column projections in this paper we examine the problem of reconstructing a discrete two dimensional set from its two orthogonal projection h v when the set satisfies some convexity conditions we show that the algorithm of the paper int j imaging systems and technol 9 1998 69 is a good heuristic algorithm but it does not solve the problem for all h v instances we propose a modification of this algorithm solving the problem for all h v instances by starting to build the spine the complexity of our reconstruction algorithm is o mn log mn min m2 n2 in the worst case however according to our experimental results in 99 of the studied cases the algorithm is able to reconstruct a solution without using the newly introduced operation in such cases the upper bound of the complexity of the algorithm is o mn log mn a systematic comparison of this algorithm was done and the results show that this algorithm has the better average complexity than other published algorithms the way of comparison and the results are given in a separate paper linear algebra appl submitted finally we prove that the problem can be solved in polynomial time also in a class of discrete sets which is larger than the class of convex polyominoes namely in the class of 8 connected convex sets

the np completeness of a tomographical problem on bicolored domino tilings in this paper we study the problem of reconstructing a bicolored domino tiling of a rectangular surface from its horizontal and vertical projections we use a reduction from the np complete problem numerical matching with target sums in order to prove that unless p np this task cannot be performed in polynomial time the reconstruction of monochromatic domino tilings is still open

a tiling system for the class of l convex polyominoes a polyomino is said to be l convex if any two of its cells can be connected by a path entirely contained in the polyomino and having at most one change of direction in this paper answering a problem posed by castiglione and vaglica 6 we prove that the class of l convex polyominoes is tiling recognizable to reach this goal first we express the l convexity constraint in terms of a set of independent properties then we show that each class of convex polyominoes having one of these properties is tiling recognizable

isolating the dynamic attributes of musical timbre three experiments examined the dynamic attributes of timbre by evaluating the role of onsets in similarity judgments in separate experiments subjects heard complete orchestral instrument tones the onsets of those tones and tones with the onsets removed remainders ratings for complete tones corresponded to those for onsets indicating that the salient acoustic attributes for complete tones are present at the onset ratings for complete tones also corresponded to those for remainders indicating that the salient attributes for complete tones are present also in the absence of onsets subsequent acoustic analyses demonstrated that this pattern of similarity was due to the centroid frequencies and amplitude envelopes of the tones the results indicate that the dynamic attributes of timbre are not only present at the onset but also throughout and that multiple acoustic attributes may contribute to the same perceptual dimensions

reconstructing convex polyominoes from horizontal and vertical projections in 1 we studied the problem of reconstructing a discrete set 5 from its horizontal and vertical projections we defined an algorithm that establishes the existence of a convex polyomino whose horizontal and vertical projections are equal to a pair of assigned vectors h v with h m and v n its computational cost is o n4m4 in this paper we introduce some operations for recontructing convex polyominoes by means of vectors h s and v s partial sums these operations allows us to define a new algorithm whose complexity is less than o n2m2

discrimination of musical instrument sounds resynthesized with simplified spectrotemporal parameters the perceptual salience of several outstanding features of quasiharmonic time variant spectra was investigated in musical instrument sounds spectral analyses of sounds from seven musical instruments clarinet flute oboe trumpet violin harpsichord and marimba produced time varying harmonic amplitude and frequency data six basic data simplifications and five combinations of them were applied to the reference tones amplitude variation smoothing coherent variation of amplitudes over time spectral envelope smoothing forced harmonic frequency variation frequency variation smoothing and harmonic frequency flattening listeners were asked to discriminate sounds resynthesized with simplified data from reference sounds resynthesized with the full data averaged over the seven instruments the discrimination was very good for spectral envelope smoothing and amplitude envelope coherence but was moderate to poor in decreasing order for forced harmonic frequency variation frequency variation smoothing frequency flattening and amplitude variation smoothing discrimination of combinations of simplifications was equivalent to that of the most potent constituent simplification objective measurements were made on the spectral data for harmonic amplitude harmonic frequency and spectral centroid changes resulting from simplifications these measures were found to correlate well with discrimination results indicating that listeners have access to a relatively fine grained sensory representation of musical instrument sounds

reconstruction of convex polyominoes with a blocking component several papers in the available literature tackled problems concerning convex polyominoes in discrete tomography an interesting subclass consists of l convex polyominoes since the related reconstruction problem can have only a unique solution on the other hand recent studies have modeled an approach to reconstruct objects even in the case that some of the projections are unavailable due to a particularly dense part of the scanned object that we refer to as a blocking component in this work we merge the two problems in order to obtain efficient reconstruction algorithms for convex and l convex polyominoes in case a blocking component is included

polyominoes defined by two vectors abstract the polyominoes problem defined by two vectors has been proposed by m nivat in the course of the seminar held at the dipartimento di sistemi e informatica di firenze on september 1992 on the subject tiling the plane with a horizontal bar h m and a vertical bar v n it is the problem of establishing the existence of a polyomino with a given number of cells in every column and every row the problem is solved for the following classes of polyominoes directed column convex directed convex and parallelogram the problem is also solved in the class of convex polyominoes in a particular case furthermore it is possible to define an algorithm that controls the existence of a directed column convex or directed convex or parallelogram polyomino with a given number of cells in every column and in every row

on the comptational complexity of determining polyatomic structures by x rays the problem of recovering the structure of crystalline materials from their discrete x rays is of fundamental interest in many practical applications an important special case concerns determining the position of atoms of several different types in the integer lattice given the number of each type lying on each line parallel to some lattice directions we show that the corresponding consistency problem is np complete for any two or more different fixed directions when six or more types of atoms are involved

on the unique satisfiability problem unique sat is the problem of deciding whether a given boolean formula has exactly one satisfying truth assignment this problem is a typical moreover complete representative of a natural class of problems about unique solutions all these problems belong to the class dife l1 l2 l1 lz np studied by papadimitriou and yannakakis we consider the relationship between these two classes particularly whether unique sat is dife complete it is if np co np we construct an oracle relative to which unique sat is not complete for dif and another oracle relative to which unique sat is complete for dif e whereas np v co np

a reconstruction algorithm for a subclass of instances of the 2 color problem in the field of discrete tomography the 2 color problem consists in reconstructing a matrix whose elements are of two different types starting from its horizontal and vertical projections it is known that the 1 color problem admits a polynomial time reconstruction algorithm while the c color problem with c 2 is np hard thus the 2 color problem constitutes an interesting example of a problem just in the frontier between hard and easy problems in this paper we define a linear time algorithm in the size of the output matrix to solve a subclass of its instances where some values of the horizontal and vertical projections are constant while the others are upper bounded by a positive number proportional to the dimension of the problem our algorithm relies on classical studies for the solution of the 1 color problem

regular switching components abstract we consider a problem of discrete tomography which consists of reconstructing a finite lattice set s z 2 from given horizontal and vertical x rays i e with prescribed numbers of points in each row and column without additional requirements the problem can be solved in polynomial time many variants require the solution to be in a chosen class a for instance the problem is np complete for the class a h v of hv convex lattice sets and it is polynomial for the class a h v p of hv convex polyominoes twenty years after these results the problem s complexity remains unknown for a c the class of c convex lattice sets i e two dimensional lattice polytopes the main difficulty to solve this problem comes from combinatorial structures called switching components switching components are closed path with horizontal and vertical edges such that the solutions s are composed of either the elements of even or of odd indices this binary choice can be encoded by a boolean variable associated with the switching component and the convexity constraints are simply encoded by sat clauses 2 clauses for hv convexity and 3 clauses for c convexity the purpose of the paper is to investigate the properties of the switching components and the consequences of the convexity requirements we divide the switching components in two classes regular if their turning angle is constant irregular otherwise we prove that adjacent regular switching components have the same boolean values this property allows us to merge them into extended switching components we prove that if all switching components are regular then the extended switching components are all independent then the number of solutions with the considered feet is 2 n where n is the number of extended switching components finally we prove that they are geometrically ordered

tiling with bars under tomographic constraints we wish to tile a rectangle or a torus with only vertical and horizontal bars of a given length such that the number of bars in every column and row equals given numbers we present results for particular instances and for a more general problem while leaving open the initial problem

a self routing benes network and parallel permutation algorithms a benes permutation network capable of setting its own switches dynamically is presented the total switch setting and delay time for the n input utput self routing network is o log n it is shown that the network is capable of performing a rich class of permutations the self routing scheme leads to efficient o log n parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers

reconstruction of domino tiling from its two orthogonal projections we are interested in the reconstruction of a domino tiling of a rectangle from its two orthogonal projections we give polynomial algorithms for some subproblems when all the dominoes are of the same type and prove np completeness results when there are three types of dominoes when two types of dominoes are allowed we give a polynomial time transformation from a well known open problem

self routing technique in perfect shuffle networks using control tags the self routing technique using control tags on multiple pass perfect shuffle networks is generalized in particular they show that bit permute complement permutations can be realized and unscrambled in 2n 1 passes or less where n log sub 2 n n being the number of terminals on either side they also show that most of the frequently used permutations are in the intersection of omega realizing and inverse omega realizing sets and can be realized and unscrambled in n passes

three dimensional statistical data security problems suppose there is a three dimensional table of cross tabulated nonnegative integer statistics and suppose that all of the row column and file sums are revealed together with the values in some of the individual cells in the table the question arises as to whether as a consequence the values contained in some of the other suppressed cells can be deduced from the information revealed the corresponding problem in two dimensions has been comprehensively studied by gusfield siam j comput 17 1988 pp 552 571 who derived elegant polynomial time algorithms for the identification of any such compromised cells and for calculating the tightest bounds on the values contained in all cells that follow from the information revealed in this note it is shown by contrast that the three dimensional version of the problem is np complete it is also shown that if the suggested row column and file sums for an unknown three dimensional table are given with or without the values in some of the cells the problem of determining whether there exists any table with the given sums is np complete in the course of proving these results the np completeness of some constrained latin square construction problems which are of some interest in their own right is established

discrete tomography determination of finite sets by x rays we study the determination of finite subsets of the integer lattice en n 2 by x rays in this context an x ray of a set in a direction u gives the number of points in the set on each line parallel to u for practical reasons only x rays in lattice directions that is directions parallel to a nonzero vector in the lattice are permitted by combining methods from algebraic number theory and convexity we prove that there are four prescribed lattice directions such that convex subsets of en i e finite subsets f with f en n conv f are determined among all such sets by their x rays in these directions we also show that three x rays do not suffice for this purpose this answers a question of larry shepp and yields a stability result related to hammer s x ray problem we further show that any set of seven prescribed mutually nonparallel lattice directions in 22 have the property that convex subsets of 22 are determined among all such sets by their x rays in these directions we also consider the use of orthogonal projections in the interactive technique of successive determination in which the information from previous projections can be used in deciding the direction for the next projection we obtain results for finite subsets of the integer lattice and also for arbitrary finite subsets of euclidean space which are the best possible with respect to the numbers of projections used

reconstructing polyatomic structures from discrete x rays we address a discrete tomography problem that arises in the study of the atomic structure of crystal lattices a polyatomic structure t can be defined as an integer lattice in dimension d 2 whose points may be occupied by c distinct types of atoms to analyze t we conduct measurements that we call discrete x rays a discrete x ray in direction determines the number of atoms of each type on each line parallel to given such non parallel x rays we wish to reconstruct t the complexity of the problem for c 1 one atom type has been completely determined by gardner et al technical report 970 05012 techn univ munchen fak f math 1997 who proved that the problem is np complete for any dimension d 2 and 3 non parallel x rays and that it can be solved in polynomial time otherwise ryser mathematical association of america and quinn boden rahway new jersey 1963 the np completeness result above clearly extends to any c 2 and therefore when studying the polyatomic case we can assume that 2 as shown in another article by the same authors gardner et al theoret comput sci 1997 to appear this problem is also np complete for c 6 atoms even for dimension d 2 and axis parallel x rays gardner et al 1997 conjecture that the problem remains np complete for c 3 4 5 although as they point out the proof idea in gardner et al 1997 does not seem to extend to c 5 we resolve the conjecture from gardner et al 1997 by proving that the problem is indeed np complete for c 3 in 2d even for axis parallel x rays our construction relies heavily on some structure results for the realizations of 0 1 matrices with given row and column sums

detection of random alterations to time varying musical instrument spectra the time varying spectra of eight musical instrument sounds were randomly altered by a time invariant process to determine how detection of spectral alteration varies with degree of alteration instrument musical experience and spectral variation sounds were resynthesized with centroids equalized to the original sounds with frequencies harmonically flattened and with average spectral error levels of 8 16 24 32 and 48 listeners were asked to discriminate the randomly altered sounds from reference sounds resynthesized from the original data for all eight instruments discrimination was very good for the 32 and 48 error levels moderate for the 16 and 24 error levels and poor for the 8 error levels when the error levels were 16 24 and 32 the scores of musically experienced listeners were found to be significantly better than the scores of listeners with no musical experience also in this same error level range discrimination was significantly affected by the instrument tested for error levels of 16 and 24 discrimination scores were significantly but negatively correlated with measures of spectral incoherence and normalized centroid deviation on unaltered instrument spectra suggesting that the presence of dynamic spectral variations tends to increase the difficulty of detecting spectral alterations correlation between discrimination and a measure of spectral irregularity was comparatively low

conjugacy relationship between m convex and l convex functions in continuous variables by extracting combinatorial structures in well solved nonlinear combinatorial optimization problems murota 1996 1998 introduced the concepts of m convexity and l convexity to functions defined over the integer lattice recently murota shioura 2000 2001 extended these concepts to polyhedral convex functions and quadratic functions in continuous variables in this paper we consider a further extension to more general convex functions defined over the real space and provide a proof for the conjugacy relationship between general m convex and l convex functions

frames a simple characterization of permutations realized by frequently used networks rearrangeable multistage networks such as the benes network realize any permutation yet their routing algorithms are not cost effective on the other hand there exist inexpensive routing algorithms for nonrearrangeable networks but no simple technique exists to characterize all the permutations realized on these networks this paper introduces the concept of frame and shows how it can be used to characterize all the permutations realized on various multistage interconnection networks they include subnetworks of baseline benes and cascaded baseline and shuffle exchange networks

reconstruction of binary matrices under fixed size neighborhood constraints using a dynamic programming approach we prove that a large variety of matrix reconstruction problems from two projections can be solved in polynomial time whenever the number of rows or columns is fixed we also prove some complexity results for several problems concerning the reconstruction of a binary matrix when a neighborhood constraint occurs

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

acoustic structure of the five perceptual dimensions of timbre in orchestral instrument tones attempts to relate the perceptual dimensions of timbre to quantitative acoustical dimensions have been tenuous leading to claims that timbre is an emergent property if measurable at all here a three pronged analysis shows that the timbre space of sustained instrument tones occupies 5 dimensions and that a specific combination of acoustic properties uniquely determines gestalt perception of timbre firstly multidimensional scaling mds of dissimilarity judgments generated a perceptual timbre space in which 5 dimensions were cross validated and selected by traditional model comparisons secondly subjects rated tones on semantic scales a discriminant function analysis dfa accounting for variance of these semantic ratings across instruments and between subjects also yielded 5 significant dimensions with similar stimulus ordination the dimensions of timbre space were then interpreted semantically by rotational and reflectional projection of the mds solution into two dfa dimensions thirdly to relate this final space to acoustical structure the perceptual mds coordinates of each sound were regressed with its joint spectrotemporal modulation power spectrum sound structures correlated significantly with distances in perceptual timbre space contrary to previous studies most perceptual timbre dimensions are not the result of purely temporal or spectral features but instead depend on signature spectrotemporal patterns

an introduction to periodical discrete sets from a tomographical perspective in this paper we introduce a new class of binary matrices whose entries show periodical configurations and we furnish a first approach to their analysis from a tomographical point of view in particular we propose a polynomial time algorithm for reconstructing matrices with a special periodical behavior from their horizontal and vertical projections we succeeded in our aim by using a reduction involving polyominoes which can be characterized by means of 2 sat formulas

approximating the number of monomer dimer coverings of a lattice we study the problem of counting the number of coverings of ad dimensional rectangular lattice by a specified number of monomers and dimers this problem arises in several models in statistical physics and has been widely studied a classical technique due to fisher kasteleyn and temperley solves the problem exactly in two dimensions when the number of monomers is zero the dimer covering problem but is not applicable in higher dimensions or in the presence of monomers this paper presents the first provably polynomial time approximation algorithms for computing the number of coverings with any specified number of monomers ind dimensional rectangular lattices with periodic boundaries for any fixed dimensiond and in two dimensional lattices with fixed boundaries the algorithms are based on monte carlo simulation of a suitable markov chain and in constrast to most monte carlo algorithms in statistical physics have rigorously derived performance guarantees that do not rely on any assumptions the method generalizes to counting coverings of any finite vertex transitive graph a class which includes most natural finite lattices with periodic boundary conditions