a mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints this study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized these problems can be modeled as a more general job selection problem cases with resumable non resumable and semi resumable jobs as well as cases without availability constraints are investigated the proposed efficient mixed integer linear programming approach includes possible improvements to the model notably specialized lifted knapsack cover cuts the method proves to be competitive compared with existing dedicated methods numerical experiments on randomly generated instances show that all 350 job instances of the test bed are closed for the well known problem 1 r i sum w iu i for all investigated problem types 98 4 of 500 job instances can be solved to optimality within one hour

applying machine based decomposition in 2 machine flow shops abstract the shifting bottleneck sb heuristic is among the most successful approximation methods for solving the job shop problem it is essentially a machine based decomposition procedure where a series of one machine sequencing problems omsps are solved however such a procedure has been reported to be highly ineffective for the flow shop problems in particular we show that for the 2 machine flow shop problem the sb heuristic will deliver the optimal solution in only a small number of instances we examine the reason behind the failure of the machine based decomposition method for the flow shop an optimal machine based decomposition procedure is formulated for the 2 machine flow shop the time complexity of which is worse than that of the celebrated johnson s rule the contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex job shops can also be suitably modified to optimally solve the simpler flow shops

a block approach for single machine scheduling with release dates and due dates abstract the problem of scheduling jobs on a single machine subject to given release dates and due dates is considered a new algorithm of the branch and bound type for solving this problem is proposed the approach used in the paper is fully based on the eliminative properties of a block of jobs and in contradiction to the existing algorithms it does not require any heuristic method to generate a current solution in a search tree however a heuristic may be used in order to obtain a good initial solution extensive computational experiments show a high efficiency of the algorithm

a time indexed formulation of non preemptive single machine scheduling problems we consider the formulation of non preemptive single machine scheduling problems using time indexed variables this approach leads to very large models but gives better lower bounds than other mixed integer programming formulations we derive a variety of valid inequalities and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities a cutting plane branch and bound algorithm based on these inequalities has been implemented computational experience on small problems with 20 30 jobs and various constraints and objective functions is presented

linearity and solvability in multicast networks it is known that for every solvable multicast network there exists a large enough finite field alphabet such that a scalar linear solution exists we prove i every binary solvable multicast network with at most two messages has a binary scalar linear solution ii for more than two messages not every binary solvable multicast network has a binary scalar linear solution iii a multicast network that has a solution for a given alphabet might not have a solution for all larger alphabets

the symmetric traveling salesman polytope and its graphical relaxation composition of valid inequalities the graphical relaxation of the traveling salesman problem is the relaxation obtained by requiring that the salesman visit each city at least once instead of exactly once this relaxation has already led to a better understanding of the traveling salesman polytope in cornuejols fonlupt and naddef 1985 we show here how one can compose facet inducing inequalities for the graphical traveling salesman polyhedron and obtain other facet inducing inequalities this leads to new valid inequalities for the symmetric traveling salesman polytope this paper is the first of a series of three papers on the symmetric traveling salesman polytope the next one studies the strong relationship between that polytope and its graphical relaxation and the last one applies all the theoretical developments of the two first papers to prove some new facet inducing results

reversible and irreversible information networks it is shown that there exist information networks where messages can be sent utilizing network coding more easily in one direction than in the opposite direction this is valid even though each channel is assumed to have the same capacity in both directions it is shown that irreversible information networks only have solutions that use nonlinear network coding this correspondence argues that this result is more surprising than it might appear at first sight and that it follows using ideas resembling the path integral in quantum mechanics

a bisimulation for type abstraction and recursion we present a bisimulation method for proving the contextual equivalence of packages in calculus with full existential and recursive types unlike traditional logical relations either semantic or syntactic our development is elementary using only sets and relations and avoiding advanced machinery such as domain theory admissibility and tt closure unlike other bisimulations ours is complete even for existential types the key idea is to consider sets of relations instead of just relations as bisimulations

a branch and bound to minimize the number of late jobs on a single machine with release time constraints this paper presents a branch and bound algorithm for the single machine scheduling problem 1 ri ui where the objective function is to minimize the number of late jobs lower bounds based on a lagrangian relaxation and no reductions to polynomially solvable cases are proposed efficient elimination rules together with strong dominance relations are also used to reduce the search space a branch and bound exploiting these techniques solves to optimality instances with up to 200 jobs improving drastically the size of problems that could be solved by exact methods up to now

a branch and check algorithm for minimizing the weighted number of late jobs on a single machine with release dates in this paper we consider the scheduling problem of minimizing the weighted number of late jobs on a single machine 1 rj wjuj a branch and check algorithm is proposed where a relaxed integer programming formulation is solved by branch and bound and infeasible solutions are cut off using infeasibility cuts we suggest two ways to generate cuts first tightened no good cuts are derived using a modification of the algorithm by carlier 1982 ejor v 11 42 47 which was developed for the problem of minimizing maximum lateness on a single machine secondly we show how to create cuts by using constraint propagation the proposed algorithm is implemented in the mosel modelling and optimization language computational experiments on instances with up to 140 jobs are reported a comparison is presented with the exact approach of peridy at al 2003 ejor v 148 591 603

nonreversibility and equivalent constructions of multiple unicast networks we prove that for any finite directed acyclic network there exists a corresponding multiple unicast network such that for every alphabet each network is solvable if and only if the other is solvable and for every finite field alphabet each network is linearly solvable if and only if the other is linearly solvable the proof is constructive and creates an extension of the original network by adding exactly s 5m r 1 new nodes where in the original network m is the number of messages r is the average number of receiver nodes demanding each source message and s is the number of messages emitted by more than one source the construction is then used to create a solvable multiple unicast network which becomes unsolvable over every alphabet size if all of its edge directions are reversed and if the roles of source receiver pairs are reversed

the crown inequalities for the symmetric traveling salesman polytope we define a new family of valid inequalities for the symmetric traveling salesman polytope stspn that is the convex hull of the incidence vectors of all hamiltonian cycles of a complete graph with n nodes the smallest value of n for which the inequalities are defined is 8 we call these inequalities crown inequalities and we prove that they are facet inducing for stspn for n 8 we describe some extensions of the crown inequalities and we prove that they induce facets of stspn as well finally we discuss some issues on the possible applications of these inequalities in a polyhedral cutting plane algorithm

an algorithm for solving the job shop problem in this paper we propose a branch and bound method for solving the job shop problem it is based on one machine scheduling problems and is made more efficient by several propositions which limit the search tree by using immediate selections it solved for the first time the famous 10 10 job shop problem proposed by muth and thompson in 1963

proving congruence of bisimulation in functional programming languages we give a method for proving congruence of bisimulation like equivalences in functional programming languages the method applies to languages that can be presented as a set of expressions together with an evaluation relation we use this method to show that some generalizations of abramsky s applicative bisimulation are congruences whenever evaluation can be specified by a certain natural form of structured operational semantics one of the generalizations handles nondeterminism and diverging computations

facet identification for the symmetric traveling salesman polytope several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given an identification procedure accepts as input the support graph of a point which does not belong to the polytope and returns as output some of the facet inducing inequalities violated by the point a procedure which always accomplishes this task is calledexact otherwise it is calledheuristic we give exact procedures for the subtour elimination and the 2 matching constraints based on the gomory hu and padberg rao algorithms respectively efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities these procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large scale problem instances with sizes up to 2392 nodes to optimality

a branch and bound algorithm for the one machine scheduling problem with minimum and maximum time lags we consider the one machine scheduling problem with minimum and maximum time lags while minimizing the makespan this problem typically arises in a manufacturing environment where the next job has to be carried out within a specific time range after the completion of the immediately preceding job we describe a branch and bound algorithm based on the input and output of a clique and the relevant propositions for finding the optimal waiting times the computational experiments give promising results showing whether a given instance is feasible or infeasible with the proposed branch and bound algorithm we can either find an optimal schedule or establish the infeasibility within an acceptable run time

odd minimum cut sets and b matchings we show that the determination of a minimum cut set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of gomory and hu for multi terminal networks we connect this problem to the problem of identifying a matching or blossom constraint that chops off a point which is not contained in the convex hull of matchings or proving that no such inequality exists both the b matching problems without and with upper bounds are considered we discuss how the results of this paper can be used in conjunction with commercial lp packages lo solve b matching problems

networks matroids and non shannon information inequalities we define a class of networks called matroidal networks which includes as special cases all scalar linearly solvable networks and in particular solvable multicast networks we then present a method for constructing matroidal networks from known matroids we specifically construct networks that play an important role in proving results in the literature such as the insufficiency of linear network coding and the unachievability of network coding capacity we also construct a new network from the vamos matroid which we call the vamos network and use it to prove that shannon type information inequalities are in general not sufficient for computing network coding capacities to accomplish this we obtain a capacity upper bound for the vamos network using a non shannon type information inequality discovered in 1998 by zhang and yeung and then show that it is smaller than any such bound derived from shannon type information inequalities this is the first application of a non shannon type inequality to network coding we also compute the exact routing capacity and linear coding capacity of the vamos network finally using a variation of the vamos network we prove that shannon type information inequalities are insufficient even for computing network coding capacities of multiple unicast networks

the one machine problem with delayed precedence constraints and its use in job shop scheduling we study the one machine scheduling problem with release and delivery times and the minimum makespan objective in the presence of constraints that for certain pairs of jobs require a delay between the completion of the first job and the start of the second delayed precedence constraints this problem arises naturally in the context of the shifting bottleneck procedure for the general job shop scheduling problem as a relaxation of the latter tighter than the standard one machine relaxation the paper first highlights the difference between the two relaxations through some relevant complexity results then it introduces a modified longest tail heuristic whose analysis identifies those situations that permit efficient branching as a result an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one machine problem embedding this algorithm into a modified version of the shifting bottleneck procedure that uses the tighter one machine relaxa

closure solvability for network coding and secret sharing network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive given a network the network coding solvability problem decides whether all the packets requested by the destinations can be transmitted in this paper we introduce a new approach to this problem we define a closure operator on a digraph closely related to the network coding instance and we show that the constraints for network coding can all be expressed according to that closure operator thus a solution for the network coding problem is equivalent to a so called solution of the closure operator we can then define the closure solvability problem in general which surprisingly reduces to finding secret sharing matroids when the closure operator is a matroid based on this reformulation we can easily prove that any multiple unicast where each node receives at least as many arcs as there are sources solvable by linear functions we also give an alternative proof that any nontrivial multiple unicast with two source receiver pairs is always solvable over all sufficiently large alphabets based on singular properties of the closure operator we are able to generalize the way in which networks can be split into two distinct parts we also provide a new way of identifying and removing useless nodes in a network we also introduce the concept of network sharing where one solvable network can be used to accommodate another solvable network coding instance finally the guessing graph approach to network coding solvability is generalized to any closure operator which yields bounds on the amount of information that can be transmitted through a network

an exact approach for single machine subproblems in shifting bottleneck procedures for job shops with total weighted tardiness objective abstract in this paper we propose an exact solution method for single machine scheduling problems typically arising from bottleneck based decomposition of weighted tardiness job shops the encountered subproblems are characterized by delayed precedence constraints multiple local due dates per operation and an objective function that is given by a weighted sum of maximum tardiness values the key concept for solving these subproblems to optimality is a dominance rule whose underlying concepts have been newly developed to cope with the given structural properties furthermore a simple lower bound and a dedicated constraint programming technique are presented the efficiency of the proposed method is demonstrated by means of single machine problems collected during a run of a shifting bottleneck procedure for job shops in different size and due date tightness configurations

two branch and bound algorithms for the permutation flow shop problem abstract the objective of this paper is to present two exact methods for the permutation flow shop problem the first method is based on immediate selections and optimal adjustments of heads and tails the second method consists in recursively enumerating jobs potentially processed first inputs and jobs which would be processed last outputs on machines it is found that this second method gives better results than the first however the first method becomes more efficient when initial heads and tails are added

bi simulations up to characterise process semantics we define bi simulations up to a preorder and show how we can use them to provide a coinductive bi simulation like characterisation of semantic equivalences preorders for processes in particular we can apply our results to all the semantics in the linear time branching time spectrum that are defined by preorders coarser than the ready simulation preorder the relation between bisimulations up to and simulations up to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders in particular we have shown that the simulation up to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation since all of these canonical preorders are defined in an homogeneous way we can prove properties for them in a generic way as an illustrative example of this technique we generate an axiomatic characterisation of each of these canonical preorders that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time branching time spectrum whose correctness and completeness can be proved once and for all although we first prove by induction our results for finite processes then we see by using continuity arguments that they are also valid for infinite finitary processes

graph theoretical constructions for graph entropy and network coding based communications the guessing number of a directed graph digraph equivalent to the entropy of that digraph was introduced as a direct criterion on the solvability of a network coding instance this paper makes two contributions on the guessing number first we introduce an undirected graph on all possible configurations of the digraph referred to as the guessing graph which encapsulates the essence of dependence amongst configurations we prove that the guessing number of a digraph is equal to the logarithm of the independence number of its guessing graph therefore network coding solvability is no more a problem on the operations made by each node but is simplified into a problem on the messages that can transit through the network by studying the guessing graph of a given digraph and how to combine digraphs or alphabets we are thus able to derive bounds on the guessing number of digraphs second we construct specific digraphs with high guessing numbers yielding network coding instances where a large amount of information can transit we first propose a construction of digraphs with finite parameters based on cyclic codes with guessing number equal to the degree of the generator polynomial we then construct an infinite class of digraphs with arbitrary girth for which the ratio between the linear guessing number and the number of vertices tends to one despite these digraphs being arbitrarily sparse these constructions yield solvable network coding instances with a relatively small number of intermediate nodes for which the node operations are known and linear although these instances are sparse and the sources are arbitrarily far from their corresponding sinks

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

constraint propogation techniques for the disjunctive scheduling problem abstract constraint propagation is an elementary method for reducing the search space of combinatorial search and optimization problems which has become more and more important in the last decades the basic idea of constraint propagation is to detect and remove inconsistent variable assignments that cannot participate in any feasible solution through the repeated analysis and evaluation of the variables domains and constraints describing a specific problem instance the contribution of this paper is twofold the first contribution is a description of efficient constraint propagation methods also known as consistency tests for the disjunctive scheduling problem dsp which is a generalization of the classical job shop scheduling problem jsp applying an elementary constraint based approach involving a limited number of search variables we will derive consistency tests that ensure 3 b consistency we will further present and analyze both new and classical consistency tests which to some extent are generalizations of the aforementioned consistency tests involving a higher number of variables but still can be implemented efficiently with a polynomial time complexity further the concepts of energetic reasoning and shaving are analyzed and discussed the other contribution is a classification of the consistency tests derived according to the domain reduction achieved the particular strength of using consistency tests is based on their repeated application so that the knowledge derived is propagated i e reused for acquiring additional knowledge the deduction of this knowledge can be described as the computation of a fixed point since this fixed point depends upon the order of the application of the tests we first derive a necessary condition for its uniqueness we then develop a concept of dominance which enables the comparison of different consistency tests as well as a simple method for proving dominance an extensive comparison of all consistency tests is given quite surprisingly we will find out that some apparently stronger consistency tests are subsumed by apparently weaker ones at the same time an open question regarding the effectiveness of energetic reasoning is answered

absalom balancing assembly lines with assignment restrictions abstract assembly line balancing problems albps arise whenever an assembly line is configured redesigned or adjusted an albp consists of distributing the total workload for manufacturing products among the work stations along the line on the one hand research has focussed on developing effective and fast solution methods for exactly solving the simple assembly line balancing problem salbp on the other hand a number of real world extensions of salbp have been introduced but solved with straight forward and simple heuristics in many cases therefore there is a lack of procedures for exactly solving such generalized albp in this paper we show how to extend the well known solution procedure s alome scholl a klein r 1997 s alome a bidirectional branch and bound procedure for assembly line balancing informs j comput 9 319 334 which is able to solve even large salbp instances in a very effective manner to a problem extension with different types of assignment restrictions called aralbp the extended procedure referred to as a bsalom employs a favorable branching scheme an arsenal of bounding rules and a variety of logical tests using ideas from constraint programming computational experiments show that a bsalom is a very promising exact solution approach although the additional assignment restrictions complicate the problem considerably and necessitate a relaxation of some components of s alome

the one machine sequencing problem let m 1 and m 3 be non bottleneck machines and m 2 a bottleneck machine processing only one job at a time suppose that n jobs have to be processed on m 1 m 2 and m 1 in that order and job i has to spend a time a on m 1 d 1 on m 2 and q 1 on m 3 we want to minimize the makespan this problem is important since its resolution provides a bound on the makespan of complicated systems such as job shops it is np hard in the strong sense however efficient branch and bound methods exist and we describe one of them our bound for the tree search is very close to the bound used by florian et al but the principle of branching is quite different at every node we construct by an o n log n algorithm a schrage schedule then we define a critical job c a critical set j and consider two subsets of schedules the schedules when c procedes every job of j and the schedules when c follows every job of j we give the results of this method and prove that the difference between the optimum and the schrage schedule is less than d 1

entropy region and convolution the entropy region is constructed from vectors of random variables by collecting shannon entropies of all subvectors its shape is studied here by means of polymatroidal constructions notably by convolution the closure of the region is decomposed into the direct sum of tight and modular parts reducing the study to the tight part the relative interior of the reduction belongs to the entropy region behavior of the decomposition under self adhesivity is clarified results are specialized and extended to the region constructed from four tuples of random variables this and computer experiments help to visualize approximations of a symmetrized part of the entropy region the four atom conjecture on the minimal ingleton score is refuted

solution of large scale symmetric travelling salesman problems in this paper we report on a cutting plane procedure with which we solved symmetric travelling salesman problems of up to 1000 cities to optimality our implementation is based on a fast lp solver ibm s mpsx and makes effective use of polyhedral results on the symmetric travelling salesman polytope we describe the important ingredients of our code and give an extensive documentation of its computational performance

insufficiency of linear coding in network information flow it is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite field alphabet it is also known that this result does not generalize to arbitrary networks there are several examples in the literature of solvable networks with no scalar linear solution over any finite field however each example has a linear solution for some vector dimension greater than one it has been conjectured that every solvable network has a linear solution over some finite field alphabet and some vector dimension we provide a counterexample to this conjecture we also show that if a network has no linear solution over any finite field then it has no linear solution over any finite commutative ring with identity our counterexample network has no linear solution even in the more general algebraic context of modules which includes as special cases all finite rings and abelian groups furthermore we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field exactly 10 greater so the network is not even asymptotically linearly solvable it follows that even for more general versions of linearity such as convolutional coding filter bank coding or linear time sharing the network has no linear solution

adjustment of heads and tails for the job shop problem abstract the efficiency of recent enumerative methods for the job shop problem crucially depends on immediate selections of disjunctive constraints leading to adjustment of heads and tails this paper present new investigations concerning this powerful tool more efficient algorithms are proposed and global operations are introduced we also describe a new lower bound and a new branching scheme which are used to design a branch and bound method computational results show that these techniques permit to drastically reduce the size of the search trees

behavioral equivalence in the polymorphic pi calculus we investigate parametric polymorphism in message based concurrent programming focusing on behavioral equivalences in a typed process calculus analogous to the polymorphic lambda calculus of girard and reynolds polymorphism constrains the power of observers by preventing them from directly manipulating data values whose types are abstract leading to notions of equivalence much coarser than the standard untyped ones we study the nature of these constraints through simple examples of concurrent abstract data types and develop basic theoretical machinery for establishing bisimilarity of polymorphic processes we also observe some surprising interactions between polymorphism and aliasing drawing examples from both the polymorphic pi calculus and ml

core instances for testing a case study abstract data generation for computational testing of optimization algorithms is a key topic in experimental algorithmics recently concern has arisen that many published computational experiments are inadequate with respect to the way test instances are generated in this paper we suggest a new research direction that might be useful to cope with the possible limitations of data generation the basic idea is to select a finite set of instances which represent the whole set of instances we propose a measure of the representativeness of an instance which we call e representativeness for a minimization problem an instance xe is e representative of another instance x if a 1 e approximate solution to x can be obtained by solving xe focusing on a strongly np hard single machine scheduling problem we show how to map the infinite set of all instances into a finite set of e representative core instances we propose to use this finite set of e representative core instances to test heuristics

an efficient algorithm for the minimum capacity cut problem given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the two parts is minimum among all possible partitionings the standard algorithm to calculate a minimum capacity cut due to gomory and hu 1961 runs in o n4 time and is difficult to implement we present an alternative algorithm with the same worst case bound which is easier to implement and which was found empirically to be far superior to the standard algorithm we report computational results for graphs with up to 2000 nodes

fast depth based subgraph kernels for unattributed graphs in this paper we investigate two fast subgraph kernels based on a depth based representation of graph structure both methods gauge depth information through a family of k layer expansion subgraphs rooted at a vertex 1 the first method commences by computing a centroid based complexity trace for each graph using a depth based representation rooted at the centroid vertex that has minimum shortest path length variance to the remaining vertices 2 this subgraph kernel is computed by measuring the jensen shannon divergence between centroid based complexity entropy traces the second method on the other hand computes a depth based representation around each vertex in turn the corresponding subgraph kernel is computed using isomorphisms tests to compare the depth based representation rooted at each vertex in turn for graphs with n vertices the time complexities for the two new kernels are o n 2 and o n 3 in contrast to o n 6 for the classic gartner graph kernel 3 key to achieving this efficiency is that we compute the required shannon entropy of the random walk for our kernels with o n 2 operations this computational strategy enables our subgraph kernels to easily scale up to graphs of reasonably large sizes and thus overcome the size limits arising in state of the art graph kernels experiments on standard bioinformatics and computer vision graph datasets demonstrate the effectiveness and efficiency of our new subgraph kernels highlightswe investigate two fast subgraph kernels based on a depth based representation our kernels gauge depth information rooted at a vertex for a graph the time complexities for the two kernels are o n 2 and o n 3 we evaluate the performance of our subgraph kernels on standard graph datasets we demonstrate the effectiveness of the proposed subgraph kernels

upper bounds for constant weight codes let a n d w denote the maximum possible number of codewords in an n d w constant weight binary code we improve upon the best known upper bounds on a n d w in numerous instances for n spl les 24 and d spl les 12 which is the parameter range of existing tables most improvements occur for d 8 10 where we reduce the upper bounds in more than half of the unresolved cases we also extend the existing tables up to n spl les 28 and d spl les 14 to obtain these results we develop new techniques and introduce new classes of codes we derive a number of general bounds on a n d w by means of mapping constant weight codes into euclidean space this approach produces among other results a bound on a n d w that is tighter than the johnson bound a similar improvement over the best known bounds for doubly constant weight codes studied by johnson and levenshtein is obtained in the same way furthermore we introduce the concept of doubly bounded weight codes which may be thought of as a generalization of the doubly constant weight codes subsequently a class of euclidean space codes called zonal codes is introduced and a bound on the size of such codes is established this is used to derive bounds for doubly bounded weight codes which are in turn used to derive bounds on a n d w we also develop a universal method to establish constraints that augment the delsarte inequalities for constant weight codes used in the linear programming bound in addition we present a detailed survey of known upper bounds for constant weight codes and sharpen these bounds in several cases all these bounds along with all known dependencies among them are then combined in a coherent framework that is amenable to analysis by computer this improves the bounds on a n d w even further for a large number of instances of n d and w

a bisimulation for dynamic sealing we define l s e a l an untyped call by value l calculus with primitives for protecting abstract data by sealing and develop a bisimulation proof method that is sound and complete with respect to contextual equivalence this provides a formal basis for reasoning about data abstraction in open dynamic settings where static techniques such as type abstraction and logical relations are not applicable

the linear guessing number of undirected graphs abstract this paper investigates linear guessing number introduced by riis in connection with the network coding theory this paper establishes properties of linear guessing number on undirected graphs in particular lower and upper bounds for linear guessing number are established finally linear guessing numbers of product graphs are investigated

algorithms for scheduling a single machine to minimize the weighted number of late jobs this paper considers the problem of scheduling n jobs each having a processing time a due date and a weight on a single machine to minimize the weighted number of late jobs an o n log n algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero one programming formulation of the problem this linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem also a branch and bound algorithm that uses the linear programming lower bound is proposed computational results with branch and bound algorithms that use this and other lower bounds and with a dynamic programming algorithm for problems with up to 1000 jobs are given

a branch and bound algorithm with fuzzy inference for a permutation flowshop scheduling problem abstract this paper considers an m machine permutation flowshop scheduling problem of minimizing the makespan this classical scheduling problem is still important in modern manufacturing systems and is well known to be intractable i e np hard in fact branch and bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs in order to improve the performance of branch and bound algorithms this paper proposes a new dominance relation by which the search load could be reduced and notices that it is based on a sufficient precondition this suggests that the dominance relation holds with high possibility even if the precondition approximately holds thus being more realistic the branch and bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch and bound search for this purpose this paper utilizes membership functions in the context of the fuzzy inference extensive numerical experiments that were executed through monte carlo simulations and benchmark tests show that the developed branch and bound algorithm can solve 3 machine problem instances with up to 1000 jobs with probability of over 99 and 4 machine ones with up to 900 jobs with over 97

comparing object encodings recent years have seen the development of several foundational models for statically typed object oriented programming but despite their intuitive similarity differences in the technical machinery used to formulate the various proposals have made them difficult to compare using the typed lambda calculus f as a common basis we now offer a detailed comparison of four models 1 a recursive record encoding similar to the ones used by cardelli car84 reddy red88 kr94 cook coo89 chc90 and others 2 hofmann pierce and turner s existential encoding pt94 hp95 3 bruce s model based on existential and recursive types bru94 and 4 abadi cardelli and viswanathan s type theoretic encoding acv96 of a calculus of primitive objects

efficiency of reductions of job shop to flow shop problems we study the problem of scheduling n independent jobs in a job shop environment each job must be processed on at most m machines according to individual routes the objective is to minimise the maximum completion time of the jobs first the job shop problem is reduced to a flow shop problem with job precedence constraints then an extension of johnson s rule is defined to solve it the optimality of the extended johnson s rule is proved for two machine job shop problems and the rule efficiency for some three and four machine job shop problems is shown

clique tree inequalities and the symmetric travelling salesman problem the linear programming cutting plane approach for solving the travelling salesman problem has recently proven to be highly successful cf crowder and padberg crowder h p m w padberg 1980 solving large scale symmetric travelling salesman problems to optimality management sci 26 495 509 grotschel grotschel m 1980a on the symmetric travelling salesman problem solution of a 120 city problem math programming stud 12 61 77 padberg and hong padberg m w s hong 1980 on the symmetric travelling salesman problem a computational study math programming stud 12 78 107 one of the reasons for this success is certainly the fact that instead of ordinary cutting planes gomory cuts etc problem specific cutting planes could be used which define facets of the underlying integer programming polytopes in this paper we shall define a new class of inequalities clique tree inequalities valid for the travelling salesman polytope which properly contains many of the known classes of inequalities like subtour elimination constraints 2 matching constraints comb inequalities and we show that all these new inequalities induce facets of the travelling salesman polytope since the general structure of these new inequalities is quite simple we hope that it will be possible to use the inequalities efficiently in cutting plane procedures for the travelling salesman problem

notions of computation and monads abstract the calculus is considered a useful mathematical tool in the study of programming languages since programs can be identified with terms however if one goes further and uses conversion to prove equivalence of programs then a gross simplification is introduced programs are identified with total functions from values to values that may jeopardise the applicability of theoretical results in this paper we introduce calculi based on a categorical semantics for computations that provide a correct basis for proving equivalence of programs for a wide range of notions of computation

reduction and fixed points of boolean networks and linear network coding solvability linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations toward their destinations the solvability problem asks whether the demands of all the destinations can be simultaneously satisfied by using linear network coding the guessing number approach converts this problem into determining the number of fixed points of coding functions f a n to a n over a finite alphabet a usually referred to as boolean networks if a 0 1 with a given interaction graph that describes which local functions depend on which variables in this paper we generalize the so called reduction of coding functions in order to eliminate variables we then determine the maximum number of fixed points of a fully reduced coding function whose interaction graph has a loop on every vertex since the reduction preserves the number of fixed points we then apply these ideas and results to obtain four main results on the linear network coding solvability problem first we prove that non decreasing coding functions cannot solve any more instances than routing already does second we show that the triangle free undirected graphs are linearly solvable if and only if they are solvable by routing this is the first classification result for the linear network coding solvability problem third we exhibit a new class of non linearly solvable graphs fourth we determine large classes of strictly linearly solvable graphs

a non shannon type conditional inequality of information quantities given n discrete random variables spl omega x sub 1 x sub n associated with any subset spl alpha of 1 2 n there is a joint entropy h x sub spl alpha where x sub spl alpha x sub i i spl isin spl alpha this can be viewed as a function defined on 2 sup 1 2 n taking values in 0 spl infin we call this function the entropy function of spl omega the nonnegativity of the joint entropies implies that this function is nonnegative the nonnegativity of the conditional joint entropies implies that this function is nondecreasing and the nonnegativity of the conditional mutual information implies that this function is two alternative these properties are the so called basic information inequalities of shannon s information measures an entropy function can be viewed as a 2 sup n 1 dimensional vector where the coordinates are indexed by the subsets of the ground set 1 2 n as introduced by yeng see ibid vol 43 no 6 p 1923 34 1997 spl gamma sub n stands for the cone in ir 2 sup n 1 consisting of all vectors which have all these properties let spl gamma sub n be the set of all 2 sup n 1 dimensional vectors which correspond to the entropy functions of some sets of n discrete random variables a fundamental information theoretic problem is whether or not spl gamma sub n spl gamma sub n here spl gamma sub n stands for the closure of the set spl gamma sub n we show that spl gamma sub n is a convex cone spl gamma sub 2 spl gamma sub 2 spl gamma sub 3 spl ne spl gamma sub 3 but spl gamma sub 3 spl gamma sub 3 for four random variables we have discovered a conditional inequality which is not implied by the basic information inequalities of the same set of random variables this lends an evidence to the plausible conjecture that spl gamma sub n spl ne spl gamma sub n for n 3

a note on minimizing maximum lateness in a one machine sequencing problem with release dates abstract this paper deals with the problem of minimizing maximum lateness on one machine with release dates for this problem carlier 1 suggests that if a schedule obtained by schrage s algorithm is optimal then there exists a set of jobs j such that the makespan of the schrage schedule is equal to min i e j a i iej d i min i j q i where a i d i and q i is the release date processing time and the tail of job i respectively in this paper a counterexample is given for this assertion it is also shown that the assertion is true if the processing times of all the jobs are equal to one

on the index coding problem and its relation to network coding and matroid theory the index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks an instance of the index coding problem includes a sender that holds a set of information messages x x1 xk and a set of receivers r each receiver x h in r needs to obtain a message x x and has prior side information consisting of a subset h of x the sender uses a noiseless communication channel to broadcast encoding of messages in x to all clients the objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers in this paper we analyze the relation between the index coding problem the more general network coding problem and the problem of finding a linear representation of a matroid in particular we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem specifically we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions

a bisimulation like proof method for contextual properties in untyped λ calculus with references and deallocation we develop a general method for proving properties of programs under arbitrary contexts including but not limited to observational equivalence space improvement and a form of memory safety of the programs in untyped call by value l calculus with first class dynamically allocated higher order references and deallocation the method generalizes sumii et al s environmental bisimulation technique and gives a sound and complete characterization of each proved property in the sense that the bisimilarity the largest set satisfying the bisimulation like conditions equals the set of terms with the property to be proved we give examples of contextual properties concerning typical data structures such as linked lists binary search trees and directed acyclic graphs with reference counts all with deletion operations that release memory this shows the scalability of the environmental approach from contextual equivalence to other binary relations such as space improvement and unary predicates such as memory safety as well as to languages with non monotone store

a procedure for the one machine sequencing problem with dependent jobs abstract the problem of minimizing the makespan on one machine with possible dependencies between jobs is considered we enlarge the notion of precedence constraint by considering a minimal duration between the start times of each pair of dependent jobs we propose an exact algorithm where this duration is taken into account this algorithm is based on carlier s algorithm 2 closely related to that of mcmahon and florian 10 for the one machine sequencing oms problem with independent jobs computational results are reported showing the efficiency of our procedure

time lag size in multiple operations flow shop scheduling heuristics this paper considers a multistage flow shop where jobs require multiple operations at each stage and a finish to start time lag between any two consecutive operations of a job the next operation of a job cannot start until the time lag after the former operation of that job has elapsed the effect of the size of this time lag is considered when studying the effectiveness of solution approaches for this problem since the problem of minimizing the makespan is shown to be np hard even for the two stage case we present a lower bound based heuristic approach that is used to construct several heuristic procedures these heuristics use lower bounds on the minimum makespan to solve the problem the effectiveness of these heuristics is empirically evaluated for various time lag sizes by solving a large number of randomly generated problems we show that the relative performance of the heuristics depends on the size of the time lag if the ratio of mean time lag and mean processing time is 20 or more heuristics that construct an active schedule perform less well than heuristics that construct a non delay schedule the opposite holds true if this ratio is smaller the performance of the widely used shortest processing time heuristic spt deteriorates quickly if the size of the time lags increases we propose instead to use the earliest finish time heuristic eft in case time lags are present eft performs much better in this case and is identical to spt if all time lags are zero the use of the lower bound based heuristics results in an improvement of the makespan performance of up to 50 as compared with the performance of some simple dispatching heuristics that take the presence of multiple operations and time lags into account this effect increases with the size of the time lags

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

a computational study with a new algorithm for the three machine permutation flow shop problem with release times abstract we consider the three machine permutation flow shop scheduling problem with release times where the objective is to minimize the maximum completion time a special solvable case is found for the f 2 r j c max problem which sharpens the boundary between easy and hard cases and can be used to compute a tight lower bound for our problem two dominance rules are generalized and applied to generating initial schedules directing the search strategy and decomposing the problem into smaller ones the branch and bound algorithm proposed here combines an adaptive branching rule with a fuzzy search strategy to narrow the search tree and lead the search to an optimal solution as early as possible our extensive numerical experiments have led to a classification of easy vs hard problems dependent only on the relative size of the release times the algorithm has quickly solved approximately 90 of the hardest test problem instances with up to 200 jobs and 100 of the large problems classified as easy

reduction of job shop problems to flow shop problems with precedence constraints we study the problem of scheduling n independent jobs in a job shop environment each job must be processed on m machines according to individual routes the objective is to minimize the maximum completion time of the jobs first the job shop problem is reduced to a flow shop problem with job precedence constraints then a set of flow shop algorithms are modified to solve it to evaluate the quality of these heuristics several lower bounds on the optimal solution have been computed and compared with the heuristic solutions for 3040 problems the heuristics appear especially promising for job shop problems with flow like properties

proof techniques for cryptographic processes contextual equivalences for cryptographic process calculi like the spi calculus can be used to reason about correctness of protocols but their definition suffers from quantification over all possible contexts here we focus on two such equivalences namely may testing and barbed equivalence and investigate tractable proof methods for them to this aim we design an enriched labelled transition system where transitions are constrained by the knowledge the environment has of names and keys the new transition system is then used to define a trace equivalence and a weak bisimulation equivalence that avoid quantification over contexts our main results are soundness and completeness of trace and weak bisimulation equivalence with respect to may testing and barbed equivalence respectively they lead to more direct proof methods for equivalence checking the use of these methods is illustrated with a few examples concerning implementation of secure channels and verification of protocol correctness