lattice codes for deletion and repetition channels the construction of deletion codes for the editing metric is reduced to the construction of codes over the integers for the manhattan metric by run length coding the latter codes are constructed by expurgation of lattices translates these lattices in turn are obtained from construction a applied to binary codes and mathbb z 4 codes a lower bound on the size of our codes for the manhattan distance are obtained through generalized theta series of the corresponding lattices for any fixed number of deletions provided the number of runs is large enough our method supplies a correction technique for fixed number of runs and binary sequence length large our lattice construction is shown to be tight up to constants

the 1 vertex transfer matrix and accurate estimation of channel capacity the notion of a 1 vertex transfer matrix for multidimensional codes is introduced it is shown that the capacity of such codes or the topological entropy can be expressed as the limit of the logarithm of spectral radii of 1 vertex transfer matrices storage and computations using the 1 vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix the method is applied to estimate the first 15 digits of the entropy of the 2 d 0 1 run length limited channel a large scale computation of eigenvalues for the 0 1 run length limited channel in 2 d and 3 d have been carried out this was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with this in turn leads to improvements on the best previous lower and upper bounds for these channels

the positive capacity region of two dimensional run length constrained channels a binary sequence satisfies a one dimensional d k constraint if every run of zeros with possible exception of the first and the last runs has length at least d and at most k a binary two dimensional array satisfies a d k constraint if each row and each column satisfies the one dimensional d k constraint few models have been proposed in the literature to handle two dimensional data the diamond model the square model the hexagonal model and the triangular model the constraints in the different directions might be asymmetric and hence many kind of constraints are defined depending on the number of directions in the model for example a two dimensional array in the diamond model satisfies a d1 k1 d2 k 2 constraint if it satisfies the one dimensional d1 k1 constraint horizontally and the one dimensional d 2 k2 constraint vertically in this correspondence the region in which the capacity is zero or positive in the various models is examined asymmetric constraints in the diamond model and symmetric constraints in the other models are considered in particular an almost complete solution for asymmetric constraints in the diamond model is provided

a branch and bound algorithm to minimize the number of late jobs in a permutation flow shop abstract the problem of scheduling n jobs in an m machine permutation flow shop is considered each job requires processing on machines 1 m in that order the processing order of jobs is to be the same for each machine a due date for each job is specified that represents the time by which it should ideally be completed the objective is to schedule the jobs so that the number completed after their due dates is minimized a lower bound which is obtained by solving a single machine subproblem is derived also two improvement procedures which consider all subproblems together are developed a branch and bound algorithm that uses these lower bounds is described computational experience with the algorithm is reported

exact and asymptotic features of the edge density profile for the one component plasma in two dimensions there is a well known analogy between the laughlin trial wave function for the fractional quantum hall effect and the boltzmann factor for the two dimensional one component plasma the latter requires continuation beyond the finite geometry used in its derivation we consider both disk and cylinder geometry and focus attention on the exact and asymptotic features of the edge density at the special coupling gamma q 2 k bt 2 the system is exactly solvable in particular the k point correlation can be written as a k times k determinant allowing the edge density to be computed to first order in gamma 2 a double layer structure is found which in turn implies an overshoot of the density as the edge of the leading support is approached from the interior asymptotic analysis shows that the deviation from the leading order step function value is different for the interior and exterior directions for general gamma a gaussian fluctuation formula is used to study the large deviation form of the density for n large but finite this asymptotic form involves thermodynamic quantities which we independently study and moreover an appropriate scaling gives the asymptotic decay of the limiting edge density outside of the plasma

large deviation eigenvalue density for the soft edge laguerre and jacobi β ensembles we analyze the eigenvalue density for the laguerre and jacobi ensembles in the cases that the corresponding exponents are extensive in particular we obtain the asymptotic expansion up to terms o 1 in the large deviation regime outside the limiting interval of support as found in recent studies of the large deviation density for the gaussian ensemble and laguerre ensemble with fixed exponent there is a scaling from this asymptotic expansion to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge

a genetic algorithm for an industrial multiprocessor flow shop scheduling problem with recirculation abstract we propose in this paper an effective heuristic algorithm to solve a scheduling problem that comes from industry the workshop is an hybrid flow shop with recirculation and the problem is to perform jobs between a release date and a due date in order to minimize the weighted number of tardy jobs firstly an integer linear programming formulation of the problem is proposed then a lower bound a greedy algorithm and a genetic algorithm are described as approximate methods to evaluate these heuristics experiences on instances like industrial ones are computed and show the efficiency of the genetic algorithm

capacity achieving code constructions for two classes of d k constraints this correspondence presents two variable rate encoding algorithms that achieve capacity for the d k constraint when k 2d 1 or when k d 1 is not prime the first algorithm symbol sliding is a generalized version of the bit flipping algorithm introduced by aviran in addition to achieving capacity for d 2d 1 constraints it comes close to capacity in other cases the second algorithm is based on interleaving and is a generalized version of the bit stuffing algorithm introduced by bender and wolf this method uses fewer than k d biased bit streams to achieve capacity for d k constraints with k d 1 not prime in particular the encoder for d d 2 sup m 1 constraints 2 spl les m spl infin requires only m biased bit streams

flowshop scheduling with identical jobs and uniform parallel machines the single stage scheduling problem to minimize the makespan of identical jobs on uniform parallel machines is known to be solvable in polynomial time we extend this work to consider multi stage systems with flowshop configuration we show that the 2 stage problem may also be solved in polynomial time and for the number of stages greater than two the problem is shown to be np hard we present a branch and bound procedure which provides an optimal solution to the 3 stage problem and a fast heuristic procedure that is shown to provide good approximate solutions on sample problems this heuristic is a natural extension of the 2 stage polynomial time procedure we develop theoretical bounds showing that the maximum deviation between the solution derived by the heuristic procedure and the optimal solution is bounded by the maximum processing time of a machine at the second stage independent of the number of jobs and the processing times at the first and third stages we also show that the heuristic provides an approximate solution bounded by a ratio of 1 75 to the optimal solution

on runlength codes several results on binary d k codes are given first a novel derivation for the capacity of these codes based on information theoretic principles is given based on this result the spectrum of a d k code is computed finally the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the d k constraint is considered lower bounds on the capacity of such a channel are derived

constant weight and constant charge binary run length limited codes constant weight and constant charge binary sequences with constrained run length of zeros are introduced the weight and charge distribution for these sequences are found next recurrent and direct formulas for calculating the number of these sequences are obtained by considering these numbers of constant weight and constant charge run length limited rll sequences as coefficients of convergent power series generating functions are derived the fact that generating function for enumerating constant charge rll sequences does not have a closed form is proved subsequently implementation of encoding and decoding procedures using cover s enumerative scheme is shown based on the obtained results some examples such as enumeration of running digital sum rds constrained rll sequences or peak shifts control capability are also provided

runlength limited codes for single error detection in the magnetic recording channel an arithmetic function that assigns the value 0 1 or 2 to each binary sequence is introduced the authors call this function the error check value two sequences that differ by a single symmetric error or a single shift error are shown to have different error check values runlength limited codes for detecting single errors are designed by taking a set of the constrained sequences such that each code sequence has the same error check value systematic runlength limited codes that detect single errors are constructed based on the error check value it is shown that these systematic runlength limited codes have the shortest parity length possible for a single error detecting code

vicious random walkers in the limit of a large number of walkers the vicious random walker problem on a line is studied in the limit of a large number of walkers the multidimensional integral representing the probability that thep walkers will survive a timet denotedp is shown to be analogous to the partition function of a particular one component coulomb gas by assuming the existence of the thermodynamic limit for the coulomb gas one can deduce asymptotic formulas forp in the large p large t limit a straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration this event is termed a reunion consequently asymptotic formulas for the conditional probability of a reunion given that all walkers survive are derived also an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet given that allp walkers survive is calculated in the limitt p

binary convolutional codes with application to magnetic recording calderbank heegard and ozarow 1 have suggested a method of designing codes for channels with intersymbol interference such as the magnetic recording channel these codes are designed to exploit intersymbol interference the standard method is to minimize intersymbol interference by constraining the input to the channel using run length limited sequences calderbank heegard and ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function 1 d n 2 where the channel inputs are constrained to be pm 1 this problem is considered here channel inputs are generated using a nontrivial coset of a binary convolutional code the coset is chosen to limit the zero run length of the output of the channel and so maintain clock synchronization the minimum squared euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code an interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic

a new approach to constructing optimal block codes for runlength limited channels the paper describes a technique for constructing fixed length block codes for d k constrained channels the codes described are of the simplest variety codes for which the encoder restricted to any particular channel state is a one to one mapping and which is not permitted to look ahead to future messages such codes can be decoded with no memory and no anticipation and are thus an example of what schouhamer immink 1992 has referred to as block decodable for a given blocklength n and given values of d k the procedure constructs a code with the highest possible rate among all such block codes and it does so without the iterative search that is typically used i e franaszek s recursive elimination algorithm the technique used is similar to beenker and immink s 1983 construction 2 in that every message is associated with a d k l r sequence of length n d however the values used in the present approach are l k d and r k 1 as opposed to beenker and schouhamer immink s values of l r k d thus the present approach demonstrates that construction 2 is optimal for d 1 but is suboptimal for d 1 furthermore the structure of the present codes permits enumerative coding techniques to simplify encoding and decoding

a method to calculate correlation functions for β 1 random matrices of odd size the calculation of correlation functions for 1 random matrix ensembles which can be carried out using pfaffians has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size n this same complication is present in the calculation of the correlations for the ginibre orthogonal ensemble of real gaussian matrices in fact the methods used to compute the 1 n odd correlations break down in the case of n odd real ginibre matrices necessitating a new approach to both problems the new approach taken in this work is to deduce the 1 n odd correlations as limiting cases of their n even counterparts when one of the particles is removed towards infinity this method is shown to yield the correlations for n odd real gaussian matrices

on the variable common due date minimal tardy jobs bicriteria two machine flow shop problem with ordered machines we consider a special case of the ordinary np hard two machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs in panwalkar and koulamas 2012 5 the authors presented quadratic algorithm for the problem when each job has its smaller processing time on the first machine in this note we improve the running time of the algorithm to o n log n by efficient implementation using recently introduced modified binary tree data structure

writing sequences on the plane the problem of arranging two dimensional arrays of data into one dimensional sequences comes up in image processing color quantization and optical and magnetic data recording a good arrangement should enable the one dimensional sequences to be modeled as markov chains or shifts of finite type since this is not possible in general two dimensional data is most commonly scanned by rows columns or diagonals we look into three unusual ways to write a sequence in the plane by penrose tilings by space filling curves and by cylindrical and spiral lattices we show how penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces

correction to a note on the shannon capacity of runlength limited codes two remarks in the above titled paper by j ashley and p h siegel see ibid vol 33 no 4 p 601 5 july 1987 pertaining to the rationality of the base b capacity of d k runlength limited rll constraints and d k c charge constrained rll constraints where b 2 are corrected

minimizing tardy jobs in a flowshop with common due date abstract this paper considers the two machine flowshop scheduling problem where the total time for which a shop is available to complete a given number of jobs is constrained to a known number this problem is equivalent to the flowshop scheduling problem to minimize the total number of tardy jobs against a common due date it has been recently proven to be np hard in the ordinary sense a compact multidimensional knapsack problem formulation of the problem is introduced together with several structural properties a branch and bound procedure is proposed to find an optimal solution to the problem computational results show that the proposed algorithm is capable of finding optimal solutions to problems with up to 900 jobs

generalized belief propagation for the noiseless capacity and information rates of run length limited constraints the performance of the generalized belief propagation algorithm to compute the noiseless capacity and mutual information rates of finite size two dimensional and three dimensional run length limited constraints is investigated in both cases the problem is reduced to estimating the partition function of graphical models with cycles the partition function is then estimated using the region based free energy approximation technique for each constraint a method is proposed to choose the basic regions and to construct the region graph which provides the graphical framework to run the generalized belief propagation algorithm simulation results for the noiseless capacity of different constraints as a function of the size of the channel are reported in the cases that tight lower and upper bounds on the shannon capacity exist convergence to the shannon capacity is discussed for noisy constrained channels simulation results are reported for mutual information rates as a function of signal to noise ratio

partial characterization of the positive capacity region of two dimensional asymmetric run length constrained channels a binary sequence satisfies a one dimensional d k run length constraint if every run of zeros has length at least d and at most k a two dimensional binary pattern is d sub 1 k sub 1 d sub 2 k sub 2 constrained if it satisfies the one dimensional d sub 1 k sub 1 run length constraint horizontally and the one dimensional d sub 2 k sub 2 run length constraint vertically for given d sub 1 k sub 1 d sub 2 and k sub 2 the asymmetric two dimensional capacity is defined as c sub d1 k1 d2 k2 lim sub m n spl rarr spl infin 1 mn log sub 2 n sub m n sup d1 k1 d2 k2 where n sub m n sup d1 k1 d2 k2 denotes the number of d sub 1 k sub 1 d sub 2 k sub 2 constrained m spl times n binary patterns we determine whether the capacity is positive or is zero for many choices of d sub 1 k sub 1 d sub 2 k sub 2

sofic systems and encoding data techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input restricted channels this generalizes the earlier work of adler coppersmith and hassner on the same problem

block codes for the hard square model the hard square model is a two dimensional 2 d constrained system consisting of all binary arrays on a rectangular grid in which 1 s are isolated both horizontally and vertically this paper proposes algorithms to search for single state and finite state block codes with rectangular codewords that satisfy the hard square constraint although the codeword size is small single state block codes with coding rates larger than 0 5 can be designed letting the 2 d constrained sequences have finite memory increases the achievable coding rate a method for designing low complexity encoders and decoders is also presented when the codeword size increases the coding rate asymptotically approaches the capacity but with rapidly increasing complexity of the encoder and decoder

variable length state splitting with applications to average runlength constrained arc codes a new class of constrained systems average runlength constraints arcs is defined by requiring that the sum of n consecutive run lengths be bounded above by a linear function of n in particular the running average runlength of every sequence in the system is bounded above by a constant a general result is given on the capacity of arc systems the state splitting algorithm is then improved for variable length graphs this is then applied to obtain high fixed rate codes from the free binary source to arc systems as an example a rate 1 2 d k

fluctuation formula for complex random matrices a gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case where the statistic is rotationally invariant for a general linear statistic without this symmetry coulomb gas theory is used to predict that the distribution will again be a gaussian with a specific mean and variance the variance splits naturally into a bulk and surface contibution the latter resulting from the long range correlations at the boundary of the support of the eigenvalue density

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

the construction of m ary d spl infin codes that achieve capacity and have the fewest number of encoder states the existence of 100 efficient i e capacity achieving fixed rate codes for input constrained noiseless channels is guaranteed provided the channel has rational capacity a class of m ary runlength limited m d spl infin constraints was shown in previous work to have rational capacity in this correspondence we present a code construction procedure for obtaining 100 efficient codes with the fewest number of encoder states for all m d spl infin constraints with rational capacity the decoders are sliding block decoders with sliding window size d 1

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

branch and bound algorithm for the flow shop with multiple processors abstract the sequencing of a flow shop with multiple processors at each stage is a general case of the flow shop problem it involves sequencing n jobs in a flow shop where for at least one stage the facility has one or more identical machines the purpose of this paper is to present a branch and bound algorithm to solve scheduling problems of such facilities for optimizing the maximum completion time the lower bounds and elimination rules developed in this research are based upon the generalization of the flow shop problem furthermore a computational algorithm along with results is also presented the branch and bound algorithm can also be used to optimize other measures of performance in a flow shop with multiple processors

generating functions and lower bounds on rates for limited error correcting codes runlength limited rll and digital sum limited dsl codes are considered for these codes the finite and asymptotic lower bounds on achievable rates for the given minimum hamming distance are derived using generating functions and trellis diagram techniques the authors prove the existence of rll and dsl codes of rate r and minimum distance d delta n such that r or 2 log lambda sub 1 0 min log lambda sub 1 z delta log z 0

bounds on the capacity of the bit shift magnetic recording channel a simple statistical channel model is suggested to account for single position bit shifts that have been identified as one of the major impairments in magnetic recording the authors investigate bounds on the capacity of this channel where the channel inputs are the d k codes commonly used in magnetic recordings for d or 2 this channel is conveniently described in terms of phrase lengths where a bit shift causes a phrase either to shrink or to expand the inherent correlation present in consecutive shift affected phrases introduces memory into the channel model sequences of nondecreasing lower bounds and nonincreasing upper bounds on the capacity are evaluated and investigated for a variety of parameters lower bounds on the zero error capacity are also studied the channel model is extended to a concatenated scheme of a bit shift channel connected in tandem with the binary symmetric channel thus capturing both major error generating mechanisms the bit shifts as well as randomly generated errors lower and upper bounds on the capacity of this concatenated channel model with d k input sequences are derived and discussed

on row by row coding for 2 d constraints a constant rate encoder decoder pair is presented for a fairly large family of two dimensional 2 d constraints encoding and decoding is done in a row by row manner and is sliding block decodable essentially the 2 d constraint is turned into a set of independent and relatively simple one dimensional 1 d constraints this is done by dividing the array into fixed width vertical strips each row in the strip is seen as a symbol and a graph presentation of the respective 1 d constraint is constructed the maxentropic stationary markov chain on this graph is next considered a perturbed version of the corresponding probability distribution on the edges of the graph is used in order to build an encoder which operates in parallel on the strips this perturbation is found by means of a network flow with upper and lower bounds on the flow through the edges a key part of the encoder is an enumerative coder for constant weight binary words a fast realization of this coder is shown using floating point arithmetic

perfect d k codes capable of correcting single peak shifts codes for the multibit peak shift recording channel called d k codes of reduced length n are considered arbitrary d k and perfect d k codes capable of correcting single peak shifts of given size t are defined for the construction of perfect codes a general combinatorial method connected with finding good weight sequences in abelian groups is used and the concept of perfect t shift n designs is introduced explicit constructions of such designs for t 1 t 2 and t p 1 2 are given where p is a prime this construction is universal in that it does not depend on the d k constraints it also allows automatic correction of those peak shifts that violate d k constraints the construction is extended to d k codes of fixed binary length and allows the beginning of the next codeword to be determined the question whether the designed codes can be represented as systematic codes with minimal redundancy is considered as well

capacity bounds for the three dimensional 0 1 run length limited channel the capacity c sub 0 1 sup 8 of a three dimensional 0 1 run length constrained channel is shown to satisfy 0 522501741838 spl les c sub 0 1 sup 8 spl les 0 526880847825

fluctuations of eigenvalues of random normal matrices in this article we consider a fairly general potential in the plane and the corresponding boltzmann gibbs distribution of eigenvalues of random normal matrices as the order of the matrices tends to infinity the eigenvalues condensate on a certain compact subset of the plane the droplet we prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a gaussian field and we discuss various ramifications of this result

integer programming formulations of vehicle routing problems abstract various mathematical formulations are available for situations represented by vehicle routing problems the assignment based integer programming formulations of these problems are more common and easy to understand such formulations are discussed in this paper and a much simpler formulation for the vechicle routing problem is presented for the case when all the vehicles have the same load capacity and maximum allowable cost per route

a constraint generation approach for two machine shop problems with jobs selection abstract we consider job selection problems in two stage flow shops and job shops the aim is to select the best job subset with a given cardinality to minimize the makespan these problems are known to be ordinary np hard and the current state of the art algorithms can solve flow shop problems with up to 3000 jobs we introduce a constraint generation approach to the integer linear programming ilp formulation of these problems according to which the constraints associated with nearly all potential critical paths are relaxed and then only the ones violated by the relaxed solution are sequentially reinstated the proposed approach is capable of solving problems with up to 100 000 jobs

block pickard models for two dimensional constraints in pickard random fields prf the probabilities of finite configurations and the entropy of the field can be calculated explicitly but only very simple structures can be incorporated into such a field given two markov chains describing a boundary an algorithm is presented which determines whether a prf consistent with the distribution on the boundary and a 2 d constraint exists iterative scaling is used as part of the algorithm which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists a prf is defined for the domino tiling constraint represented by a quaternary alphabet prf models are also presented for higher order constraints including the no isolated bits n i b constraint and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols

minimizing late jobs in the general one machine scheduling problem abstract in this paper the problem of minimizing the number of late jobs on one machine is investigated the general problem is considered i e with release dates and different due dates a lower bound is first proposed based on the relaxation of a mixed integer linear programming formulation of the problem a heuristic is then presented its effectiveness is computationally studied by comparison with the lower bound

formulations and benders decomposition algorithms for multidepot salesmen problems with load balancing this paper describes new models and exact solution algorithms for the fixed destination multidepot salesmen problem defined on a graph with n nodes where the number of nodes each salesman is to visit is restricted to be in a predefined range such problems arise when the time to visit a node takes considerably longer as compared to the time of travel between nodes in which case the number of nodes visited in a salesman s tour is the determinant of their load the new models are novel multicommodity flow formulations with o n 2 binary variables which is contrary to the existing formulations for the same and similar problems that typically include o n 3 binary variables the paper also describes benders decomposition algorithms based on the new formulations for solving the problem exactly results of the computational experiments on instances derived from tsplib show that some of the proposed algorithms perform remarkably well in cases where formulations solved by a state of the art optimization code fail to yield optimal solutions within reasonable computation time

an o n2 algorithm for the variable common due date minimal tardy jobs bicriteria two machine flow shop problem with ordered machines abstract we consider the ordinary np hard two machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs we present an o n 2 algorithm for the problem when the machines are ordered that is when each job has its smaller processing time on the first second machine we also discuss the applicability of the proposed algorithm to the corresponding single objective problem in which the common due date is given

optimal block type decodable encoders for constrained systems a constrained system is presented by a finite state labeled graph for such systems we focus on block type decodable encoders comprising three classes known as block block decodable and deterministic encoders franaszek 1968 gives a sufficient condition which guarantees the equality of the optimal rates of block decodable and deterministic encoders for the same block length we introduce another sufficient condition called the straight line condition which yields the same result run length limited rll d k and maximum transition run mtr j k constraints are shown to satisfy both conditions in general block type decodable encoders are constructed by choosing a subset of states of the graph to be used as encoder states such a subset is known as a set of principal states for each type of encoder and each block length a natural problem is to find a set of principal states which maximizes the code rate we show how to compute the asymptotically optimal sets of principal states for deterministic encoders and how they are related to the case of large but finite block lengths we give optimal sets of principal states for mtr j k block type decodable encoders for all codeword lengths finally we compare the code rate of nonreturn to zero inverted nrzi encoders to that of corresponding nonreturn to zero nrz and signed nrzi encoders

heuristics for a flowshop scheduling problem with stepwise job objective function abstract in this work we introduce the flowshop scheduling problem with delivery dates and cumulative payoffs this problem is a variation of the flowshop scheduling problem with job release dates that maximizes the total payoff with a stepwise job objective function this paper contributes towards proposing a mathematical formulation for this new problem and an original constructive heuristic additionally we develop a new benchmark of 300 hard instances which are available in a public repository besides we provide primal and dual bounds for them extensive computational experiments were carried out taking into account classical constructive heuristics and hybrid local searches results show the merit of the ff heuristic when compared to other classical heuristics for flowshop scheduling problems additionally we compare an iterated local search ils an iterated greedy search igs and a biased random key genetic algorithm brkga both customized for the studied problem and a commercial mixed integer programming solver the comparison between these methods showed that the brkga starting with a solution from ff heuristic is able to find the best solutions in a very short period of time iterated local search and the commercial solver presented significantly worse results than the aforementioned methods

reliable communications across parallel asynchronous channels with arbitrary skews transmissions across asynchronous communication channels are subject to delay injection attacks which can cause an arbitrary number of skews that is such attacks can cause an arbitrary number of transmitted signals to arrive after the first signal of the next transmission has arrived the common assumption that despite the delays all signals from the i th transmission arrive at the decoder before any signal from the i 2 text nd transmission arrives is called a no switch assumption this paper presents a self synchronizing zero latency zero error coding scheme that requires no acknowledge and can decode transmissions distorted by an arbitrary number of skews that obey this no switch assumption the rate associated with the coding scheme provides a lower bound of 0 6942 for the zero error capacity of such a channel it is further shown that zero error channel capacity of the channel is upper bounded by 0 7248 finally this paper presents bounds on the zero error capacity of a channel for which the number of transmissions that can mix with one another is large

a node current based 2 index formulation for the fixed destination multi depot travelling salesman problem abstract the travelling salesman problem forms a basis for many optimisation problems in logistics finance and engineering several variants exist to accommodate for different problem types in this paper we discuss the fixed destination multi depot travelling salesman problem where several salesmen will start from different depots and they are required to return to the depot they originated from we propose a novel formulation for this problem using 2 index binary variables and node currents and compare it to other 2 index formulations from the literature this novel formulation requires less binary variables and continuous variables to formulate a problem resulting in lower computation times using a large benchmark the effectiveness of the new formulation is demonstrated

finite size corrections to the free energy of coulomb systems with a periodic boundary condition classical coulomb systems ind dimensions d 2 with a periodic boundary condition periodw in the directionx d are considered with the other directions of the confining volume of lengthl it is shown that if the system is in a conducting phase then the strip free energyktf w f w liml l d 1 log z has the large w expansion f w sim wf infty frac d 2 1 gamma d 2 1 pi d 2 w d 1 zeta d o left frac 1 w d 1 right wherektf is the bulk free energy per unit volume x denotes the riemann zeta function and x denotes the gamma function with 1 w identified askt this result is precisely the low temperature behavior of the free energy of a d 1 dimensional debye solid this fact is explained in terms of an equivalence between the coulomb gas and quantum fields also the expansion is verified for some exactly solved models of coulomb systems in two dimensions

on the capacity of binary and gaussian channels with run length limited inputs bounds on the capacity of binary symmetric channels and additive gaussian channels with run length limited two level binary bipolar inputs are presented and their tightness is demonstrated for some cases stationary input sequences which do not degrade capacity are considered when deriving the bounds lower bounds on the magnetic recording density for a simple continuous time recording model incorporating a minimal intertransition constraint are evaluated for soft and hard decisions a superiority of about 1 5 db in signal to noise ratio is observed for the soft decision scheme

a coding scheme for single peak shift correction in d k constrained channels a two step coding scheme for peak shift correction in d k constrained sequences is described the first step is based on q ary q k d 1 is a prime block codes that allow correction of specific types of double errors caused by single peak shifts the second step is a simple conversion of q ary symbols to binary strings of the type 00 01 the concatenation of these strings satisfies the d k constraint within the codeword and in concatenation with neighboring words the length of the codewords is controlled and if necessary can be fixed the rate r sub 1 of the overall encoding approaches 2 log sub 2 k d 1 k d 2 for large codeword lengths codes for correction of peak shift deletions and insertions of zeros are presented as well encoding and decoding are done by simple algorithms without using look up tables enumeration or denumeration procedures and therefore the codelength may be large

translation symmetry breaking in the one component plasma on the cylinder the two dimensional one component plasma i e the system of point like charged particles embedded in a homogeneous neutralizing background is studied on the surface of a cylinder of finite circumference or equivalently in a semiperiodic strip of finite width the model has been solved exactly by choquardet al at the free fermion coupling 2 in the thermodynamic limit of an infinitely long strip the particle density turns out to be a nonconstant periodic function in space and the system exhibits long range order of the wigner crystal type the aim of this paper is to describe qualitatively as well as quantitatively the crystalline state for a larger set of couplings 2 1 2 a positive integer when the plasma is mappable onto a one dimensional fermionic theory the fermionic formalism supplemented by some periodicity assumptions reveals that the density profile results from a hierarchy of gaussians with a uniform variance but with different amplitudes the number and spatial positions of these gaussians within an elementary cell depend on the particular value of analytic results are supported by the exact solution at 1 2 and by exact finite size calculations at 2 3

transformation of multidepot multisalesmen problem to the standard travelling salesman problem abstract one type of multidepot multisalesmen problem can be transformed into a standard travelling salesman problem by cooying depots and introducing imaginary depots

entropy of bit stuffing induced measures for two dimensional checkerboard constraints a modified bit stuffing scheme for two dimensional 2 d checkerboard constraints is introduced the entropy of the scheme is determined based on a probability measure defined by the modified bit stuffing entropy results of the scheme are given for 2 d constraints on a binary alphabet the constraints considered are 2 d rll d infin for d 2 3 and 4 as well as for the constraint with a minimum 1 norm distance of 3 between 1s for these results the entropy is within 1 2 of an upper bound on the capacity for the constraint as a variation of the scheme periodic merging arrays are also considered

large n expansion for the 2d dyson gas we discuss the 1 n expansion of the free energy of n logarithmically interacting charges in the plane in an external field for some particular values of the inverse temperature this system is equivalent to the eigenvalue version of certain random matrix models where it is referred to as the dyson gas of eigenvalues to find the free energy at large n and the structure of 1 n corrections we first use the effective action approach and then confirm the results by solving the loop equation the results obtained give some new representations of the mathematical objects related to the dirichlet boundary value problem complex analysis and spectral geometry of exterior domains they also suggest interesting links with bosonic field theory on riemann surfaces gravitational anomalies and topological field theories

finite state codes a class of codes called finite state fs codes is defined and investigated the codes which generalize both block and convolutional codes are defined by their encoders which are finite state machines with parallel inputs and outputs a family of upper bounds on the free distance of a given fs code is derived a general construction for fs codes is given and it is shown that in many cases the fs codes constructed in this way have a free distance that is the largest possible catastrophic error propagation cep for fs codes is also discussed it is found that to avoid cep one must solve the graph theoretic problem of finding a uniquely decodable edge labeling of the state diagram

sequences and codes with asymmetrical runlength constraints presents a generating function for runlength limited sequences intended for binary asymmetrical channels the channel capacity for such channels is derived from this generating function the authors furthermore present selected numerical values of channel capacity for these sequences an expression for the power spectrum of binary maxentropic asymmetrical sequences is given and the influence of the asymmetry on the spectrum is investigated two new runlength limited modulation codes which are suitable for use on binary asymmetrical channels are investigated

construction of fixed length insertion deletion correcting runlength limited codes an algorithm is presented for the construction of fixed length insertion deletion correcting runlength limited rll codes in this construction binary d k constrained codewords are generated by codewords of a q ary lee metric based code it is shown that this new construction always yields better codes than known constructions the use of a q ary lee 1987 metric code q odd is based on the assumption that an error insertion deletion or peak shift has maximal size q 1 2 it is shown that a decoding algorithm for the lee metric code can be extended so that it can also be applied to insertion deletion correcting rll codes furthermore such an extended algorithm can also correct some error patterns containing errors of size more than q 1 2 as a consequence if s denotes the maximal size of an error then in some cases the alphabet size of the generating code can be s 1 instead of 2 spl middot s 1

the two dimensional one component plasma at γ 2 the semiperiodic strip the one component two dimensional plasma is studied in a strip of finite width replicated periodically parallel to the long axis of the strip exact results for the one and two particle distribution functions are found at coupling q2 kt 2 the system is inhomogeneous the one and two particle distribution functions show long range order

improved lower bounds on capacities of symmetric 2d constraints using rayleigh quotients a method for computing lower bounds on capacities of two dimensional 2d constraints having a symmetric presentation in either the horizontal or the vertical direction is presented the method is a generalization of the method of calkin and wilf siam j discrete math 1998 previous best lower bounds on capacities of certain constraints are improved using the method it is also shown how this method as well as their method for computing upper bounds on the capacity can be applied to constraints which are not of finite type additionally capacities of two families of multidimensional constraints are given exactly

capacity bounds for two dimensional asymmetric m ary 0 κ and d α runlength limited channels we present bounds on the two dimensional capacity for two sets of symmetric and asymmetric m ary runlength limited constraints based on simple constructions the bounds extend and generalize previous work on binary constraints

two dimensional runlength constrained arrays with equal horizontal and vertical constraints a binary array is a d1 k1 d2 k 2 runlength constrained array if the runs of zeros in every row and column have length at least d1 and at most k1 and the runs of ones in every row and column have length at least d2 and at most k2 such arrays arise in the context of digital storage devices writing n m n d1 k1 d2 k2 for the number of d1 k 1 d2 k2 runlength constrained arrays of size mtimesn the capacity c d1 k1 d2 k2 is defined to be limm nrarrinfin 1 mn log2n m n d1 k 1 d2 k2 let d2 be an integer such that d2 ges 1 the paper shows that c 1 d2 delta d2 d2 is positive when delta ges 2 but is zero when delta les 1

codes for zero spectral density at zero frequency corresp in pulse amplitude modulation pam digital transmission systems line encoding is used for shaping the spectrum of the encoded symbol sequence to suit the frequency characteristics of the transmission channel in particular it is often required that the encoded symbol sequence have a zero mean and spectral density vanishing at zero frequency we show that the finite running digital sum condition is a necessary and sufficient condition for this to occur the result holds in particular for alphabetic codes which are the most widely used line codes

complexity and sliding block decodability a constrained system or sofic system s is the set of symbol strings generated by the finite length paths through a finite labeled directed graph karabed and marcus 1988 extending the work of adler coppersmith and hassner 1983 used the technique of state splitting to prove the existence of a noncatastrophic rate p q finite state encoder from binary data into s for any input word length p and codeword length q satisfying p q spl les cap s the shannon 1948 capacity for constrained systems that are almost finite type they further proved the existence of encoders enjoying a stronger form of decodability namely sliding block decodability in particular their result implies the existence of a 100 efficient rate 1 2 sliding block code for the charge constrained runlength limited constraint with parameters d k c 1 3 3 an almost finite type system with capacity precisely 1 2 we describe two quite different constructions of such codes the constructions highlight connections between the problem of determining sliding block decodability of a finite state encoder and certain problems of colorability for graphs and sets using these connections we show that the problem of determining the existence of a block decodable input tag assignment for a given rate p q finite state encoder is np complete for p 1 we also prove np completeness results for several related problems in combinatorics and coding

integer linear programming formulations of multiple salesman problems and its variations in this paper we extend the classical multiple traveling salesman problem mtsp by imposing a minimal number of nodes that a traveler must visit as a side condition we consider single and multidepot cases and propose integer linear programming formulations for both with new bounding and subtour elimination constraints we show that several variations of the multiple salesman problem can be modeled in a similar manner computational analysis shows that the solution of the multidepot mtsp with the proposed formulation is significantly superior to previous approaches

two dimensional constrained coding based on tiling a new variable rate coding technique is presented for two dimensional 2 d constraints for certain constraints such as the 0 2 runlength limited rll and 3 rll constraints the technique is shown to improve on previously published lower bounds on the capacity of the constraint

a general error correcting code construction for run length limited binary channels a general method is presented for constructing a single error correcting run length limited code for the class of input restricted binary symmetric channels described by the parameters d k where d is the minimum and k the maximum number of consecutive zeros in any allowable channel input sequence upper and lower bounds on the rates of these codes are derived

on the shannon capacity of dc and nyquist free codes the design of codes which are simultaneously dc and nyquist free is considered the shannon capacity of codes that are simultaneously dc and nyquist free is tabulated as a function of the number of allowed running digital sum and alternating digital sum states for this constraint the set of possible rational capacities is shown to be 1 4 1 2 3 4 a rate 3 4 dc and nyquist free code is used to demonstrate the ability to code at the highest rational capacity available

coding for the optical channel the ghost pulse constraint we consider a number of constrained coding techniques that can be used to mitigate a nonlinear effect in the optical fiber channel that causes the formation of spurious pulses called ghost pulses specifically if b sub 1 b sub 2 b sub n is a sequence of bits sent across an optical channel such that b sub k b sub l b sub m 1 for some k l m not necessarily all distinct but b sub k l m 0 then the ghost pulse effect causes b sub k l m to change to 1 thereby creating an error such errors do not occur if the sequence of bits satisfies the following constraint for all integers k l m such that b sub k b sub l b sub m 1 we have b sub k l m 1 we call this the binary ghost pulse bgp constraint we will show however that the bgp constraint has zero capacity implying that sequences satisfying this constraint cannot carry much information consequently we consider a more sophisticated coding scheme which uses ternary sequences satisfying a certain ternary ghost pulse tgp constraint we further relax these constraints by ignoring interactions between symbols that are more than a certain distance t apart in the transmitted sequence analysis of the resulting bgp t and tgp t constraints shows that these have nonzero capacities and furthermore the tgp t constrained codes can achieve rates that are significantly higher than those for the corresponding bgp t codes we also discuss the design of encoders and decoders for coding into the bgp bgp t and tgp t constraints

codes correcting a single insertion deletion of a zero or a single peak shift codes of d k sequences of constant hamming weight are considered perfect codes correcting a single insertion deletion or peak shift are defined and shown to exist a systematic method to construct large classes of perfect codes is given a number of related problems are considered

an optimal solution method for large scale multiple traveling salesmen problems we develop an efficient branch and bound based method for solving the multiple traveling salesman problem and develop lower bounds through a lagrangean relaxation that requires computing a degree constrained minimal spanning tree a subgradient optimization procedure updates the lagrange multipliers we use fast sensitivity analysis techniques to increase the underlying graph sparsity and reduce the problem size the algorithm was tested on 416 problems with up to 500 cities and 10 salesmen we also present computational results on different data sets and parameters in order to identify the major factors that influence the performance of the developed code

constrained codes as networks of relations we address the well known problem of determining the capacity of constrained coding systems while the one dimensional case is well understood to the extent that there are techniques for rigorously deriving the exact capacity in contrast computing the exact capacity of a two dimensional constrained coding system is still an elusive research challenge the only known exception in the two dimensional case is an exact however not rigorous solution to the run length limited rll system on the hexagonal lattice furthermore only exponential time algorithms are known for the related problem of counting the exact number of constrained two dimensional information arrays we present the first known rigorous technique that yields an exact capacity of a two dimensional constrained coding system in addition we devise an efficient polynomial time algorithm for counting the exact number of constrained arrays of any given size our approach is a composition of a number of ideas and techniques describing the capacity problem as a solution to a counting problem in networks of relations graph theoretic tools originally developed in the field of statistical mechanics techniques for efficiently simulating quantum circuits as well as ideas from the theory related to the spectral distribution of toeplitz matrices using our technique we derive a closed form solution to the capacity related to the path cover constraint in a two dimensional triangular array the resulting calculated capacity is path cover is a generalization of the well known one dimensional rll constraint for which the capacity is known to be

periodic prefix synchronized codes a generating function approach a generating function method is developed in order to select synchronization markers that maximize the timing span of period 2 periodic prefix synchronized pps sync timing coding with small delay sync timing codes are used in situations where conventional data synchronization is required and data time stamps or time indices are also needed a pps code is a sync timing code in which each encoded block of data is preceded by a synchronization marker with the markers preceding successive blocks forming a periodic sequence with some period p since only pps codes with small periods can have good rates at small delays and since codes with p 1 are simply gilbert s prefix synchronized codes which have been studied previously in the literature this paper focuses on p 2 codes the generating function method which extends that used by guibas and odlyzko to analyze p 1 codes enables one to find pps codes with the largest possible timing span among codes with a given delay and rate it is found that at low delays such optimized pps codes offer significant advantages over cascaded and natural marker pps codes they also compare favorably with embedded index codes finally for asymptotically large delays it is shown that the best p 2 pps codes operate at approximately the same rate and delay but twice the timing span of the best p 1 codes

convex programming upper bounds on the capacity of 2 d constraints the capacity of 1 d constraints is given by the entropy of a corresponding stationary maxentropic markov chain namely the entropy is maximized over a set of probability distributions which is defined by some linear equalities and inequalities in this paper certain aspects of this characterization are extended to 2 d constraints the result is a method for calculating an upper bound on the capacity of 2 d constraints the key steps are as follows the maxentropic stationary probability distribution on square configurations is considered set of linear equalities and inequalities is derived from this stationarity the result is then a convex program which can be easily solved numerically our method improves upon previous upper bounds for the capacity of the 2 d no isolated bits constraint as well as certain 2 d rll constraints

bounded fluctuations and translation symmetry breaking a solvable model the variance of the particle number equivalently the total charge in a domain of length mathcal l of a one component plasma ocp on a cylinder of circumference w at the reciprocal temperature 2 is shown to remain bounded as mathcal l this exactly solvable system with average density has a density profile which is periodic with period w 1 along the axis of the infinitely long cylinder this illustrates the connection between bounded variance and periodicity in quasi one dimensional systems 1 when w the system approaches the two dimensional ocp and the variance in a domain grows like its perimeter in this limit the system is translation invariant with rapid decay of correlations

bit stuffing algorithms and analysis for run length constrained channels in two and three dimensions a rigorous derivation is given of the coding rate of a variable to variable length bit stuffing coder for a two dimensional 1 spl infin constrained channel the coder studied is nearly a fixed to fixed length algorithm then an analogous variable to variable length bit stuffing algorithm for the three dimensional 1 spl infin constrained channel is presented and its coding rate is analyzed using the two dimensional method the three dimensional coding rate is demonstrated to be at least 0 502 which is proven to be within 4 of the capacity

a note on the shannon capacity of run length limited codes corresp it is proven that 100 percent efficient fixed rate codes for run length limited rll d k and rll charge constrained d k c channels are possible in only two eases namely d k c 0 1 1 and 1 3 3 specifically the binary shannon capacity of rll d k constrained systems is shown to be irrational for all values of d k 0 leq d for rll charge constrained systems with parameters d k c the binary capacity is irrational for all values of d k c 0 leq d except 0 1 1 and 1 3 3 which both have binary capacity 1 2

new bounds on the capacity of multidimensional run length constraints we examine the well known problem of determining the capacity of multidimensional run length limited constrained systems by recasting the problem which is essentially a combinatorial counting problem into a probabilistic setting we are able to derive new lower and upper bounds on the capacity of 0 k rll systems these bounds are better than all previously known analytical bounds for k 2 and are tight asymptotically thus we settle the open question what is the rate at which the capacity of 0 k rll systems converges to 1 as k we also provide the first nontrivial upper bound on the capacity of general d k rll systems

splittings of cyclic groups and perfect shift codes a splitting m s of an additive abelian group g consists of a set of integers m and a subset s spl sub g such that every nonzero element g spl isin g can be uniquely written as m spl middot h for some m spl isin m and h spl isin s splittings m spl plusmn 1 spl middot spl middot spl middot spl plusmn k correspond to perfect k shift codes used in the analysis of run length limited codes correcting single peak shifts we shall determine the set s for splittings of cyclic groups z sub p p prime by m 1 a spl middot spl middot spl middot a sup r b spl middot spl middot spl middot b sup s and m spl plusmn 1 spl plusmn a spl middot spl middot spl middot spl plusmn a sup r spl plusmn b spl middot spl middot spl middot spl plusmn b sup s this yields new conditions on the existence of perfect 3 and 4 shift codes further it can be shown that splittings of z sub p by spl plusmn 1 spl plusmn 2 spl plusmn 3 exist exactly if z sub p is also split by 1 2 3