simultaneous column and row generation for large scale linear programs with column dependent rows in this paper we develop a simultaneous column and row generation algorithm that could be applied to a general class of large scale linear programming problems these problems typically arise in the context of linear programming formulations with exponentially many variables the defining property for these formulations is a set of linking constraints which are either too many to be included in the formulation directly or the full set of linking constraints can only be identified if all variables are generated explicitly due to this dependence between columns and rows we refer to this class of linear programs as problems with column dependent rows to solve these problems we need to be able to generate both columns and rows on the fly within an efficient solution approach we emphasize that the generated rows are structural constraints and distinguish our work from the branch and cut and price framework we first characterize the underlying assumptions for the proposed column and row generation algorithm these assumptions are general enough and cover all problems with column dependent rows studied in the literature up until now to the best of our knowledge we then introduce in detail a set of pricing subproblems which are used within the proposed column and row generation algorithm this is followed by a formal discussion on the optimality of the algorithm to illustrate our approach the paper is concluded by applying the proposed framework to the multi stage cutting stock and the quadratic set covering problems

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

decidability and complexity of petri nets with unordered data we prove several decidability and undecidability results for pn an extension of p t nets with pure name creation and name management we give a simple proof of undecidability of reachability by reducing reachability in nets with inhibitor arcs to it thus the expressive power of pn strictly surpasses that of p t nets we encode pn into petri data nets so that coverability termination and boundedness are decidable moreover we obtain ackermann hardness results for all our decidable decision problems then we consider two properties width boundedness and depth boundedness that factorize boundedness width boundedness has already been proven to be decidable here we prove that its complexity is also non primitive recursive then we prove undecidability of depth boundedness finally we prove that the corresponding place version of all the boundedness problems is undecidable for pn these results carry over to petri data nets

well structured transition systems everywhere well structured transition systems wstss are a general class of infinite state systems for which decidability results rely on the existence of a well quasi ordering between states that is compatible with the transitions in this article we provide an extensive treatment of the wsts idea and show several new results our improved definitions allow many examples of classical systems to be seen as instances of wstss

spatial and behavioral types in the pi calculus we present a framework that combines ideas from spatial logics and behavioral type systems type systems for the pi calculus are proposed where newly declared restricted names are annotated with spatial process properties predicating on those names that are expected to hold in the scope of the declaration types are akin to ccs terms and account for the process abstract behavior and shallow spatial structure type checking relies on spatial model checking but properties are checked against types rather than against processes type soundness theorems ensure that for a certain class of spatial properties well typed programs are also well annotated in the sense that processes in the scope of any restriction do satisfy the corresponding annotation at run time the considered class of properties is rather general differently from previous proposals it includes both safety and liveness ones and is not limited to invariants we also elaborate a distinction between locally and globally checkable properties

multi parameterised compositional verification of safety properties we introduce a fully automatic technique for the parameterised verification of safety properties the technique combines compositionality and completeness with support to multiple parameters and it is implemented in a tool we start with an lts based labelled transition system csp like concurrent sequential processes formalism with parallel composition and hiding operators first we equip the formalism with types and variables which enable parameterising the structure of a system and prove that the formalism remains compositional next we show how trace refinement between parameterised processes can be checked by computing structural cut offs for types this way a parameterised verification task reduces to finitely many finite state refinement checks we also provide an extension to the theory which allows for user definable universal relations this enables parameterising system topology to some extent too finally we consider the assumptions related to the approach and show that each of them is necessary for decidability

xpath satisfiability in the presence of dtds we study the satisfiability problem associated with xpath in the presence of dtds this is the problem of determining given a query p in an xpath fragment and a dtd d whether or not there exists an xml document t such that t conforms to d and the answer of p on t is nonempty we consider a variety of xpath fragments widely used in practice and investigate the impact of different xpath operators on the satisfiability analysis we first study the problem for negation free xpath fragments with and without upward axes recursion and data value joins identifying which factors lead to tractability and which to np completeness we then turn to fragments with negation but without data values establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion we show that with negation the complexity ranges from pspace to exptime moreover when both data values and negation are in place we find that the complexity ranges from nexptime to undecidable furthermore we give a finer analysis of the problem for particular classes of dtds exploring the impact of various dtd constructs identifying tractable cases as well as providing the complexity in the query size alone finally we investigate the problem for xpath fragments with sibling axes exploring the impact of horizontal modalities on the satisfiability analysis

an optimization algorithm for the vehicle routing problem with time windows based on lagrangian relaxation our paper presents a new optimization method for the vehicle routing problem with time windows vrptw the vrptw is a generalization of the vehicle routing problem where the service of a customer must start within a given time interval a so called time window our method is based on a lagrangian relaxation of the constraint set requiring that each customer must be serviced the master problem consists of finding the optimal lagrangian multipliers and the subproblem is a shortest path problem with time windows and capacity constraints the optimal multipliers are found using a method exploiting the benefits of subgradient methods as well as a bundle method the method has been implemented and tested on a series of well known benchmark problems of size up to 100 customers our algorithm turns out to be very competitive compared to algorithms considered in the literature and we have succeeded in solving several previously unsolved problems

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

a kleene theorem and model checking algorithms for existentially bounded communicating automata the behavior of a network of communicating automata is called existentially bounded if communication events can be scheduled in such a way that the number of messages in transit is always bounded by a value that depends only on the machine not the run itself we show a kleene theorem for existentially bounded communicating automata namely the equivalence between communicating automata globally cooperative compositional message sequence graphs and monadic second order logic our characterization extends results for universally bounded models where for each and every possible scheduling of communication events the number of messages in transit is uniformly bounded as a consequence we give solutions in spirit of madhusudan 2001 for various model checking problems on networks of communicating automata that satisfy our optimistic restriction

deciding safety properties in infinite state pi calculus via behavioural types in the pi calculus we consider the decidability of model checking properties expressed in shallow logic a simple spatial logic we first introduce a behavioural type system that given a pi process p that might in general be infinite control tries to extract a spatial behavioural type t in the form of a ccs term that is logically equivalent to p employing techniques based on well structured transition systems wsts we prove that model checking t f is decidable for types for a fragment of the logic that can be used to encode interesting safety and reachability properties the wsts technique we rely upon requires first endowing the considered transition system with a well quasi order then defining a finite basis for the denotation of each formula this is achieved by viewing types as forests with a well quasi order that corresponds to a form of forest embedding as a consequence of the logical equivalence between types and processes we obtain the decidability of the considered fragment of the logic for well typed pi processes we discuss un decidability and complexity of model checking also outside the considered decidable fragment of shallow logic

a heuristic method for the set covering problem we present a lagrangian based heuristic for the well known set covering problem scp the algorithm was initially designed for solving very large scale scp instances involving up to 5 000 rows an

solving airline crew scheduling problems by branch and cut the crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline s fleets the problem is especially important today since costs for flying personnel of major u s carriers have grown and now often exceed 1 3 billion a year and are the second largest item next to fuel cost of the total operating cost of major u s carriers thus even small percentage savings amount to substantial dollar amounts we present a branch and cut approach to solving to proven optimality large set partitioning problems arising within the airline industry we first provide some background related to this important application and then describe the approach for solving representative problems in this problem class the branch and cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree search algorithm that uses automatic reformulation procedures heuristics and linear programming technology to assist in the solution numerical experiments are reported for a sample of 68 large scale real world crew scheduling problems these problems include both pure set partitioning problems and set partitioning problems with side constraints these base constraints represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality an interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground

what is the effective impact of the explosive orbital growth in discrete time one dimensional polynomial dynamical systems abstract we study the distribution of periodic orbits in one dimensional two parameter maps specifically we report an exact expression to quantify the growth of the number of periodic orbits for discrete time dynamical systems governed by polynomial equations of motion of arbitrary degree in addition we compute high resolution phase diagrams for quartic and for both normal forms of cubic dynamics and show that their stability phases emerge all distributed in a similar way preserving a characteristic invariant ordering such coincidences are remarkable since our exact expression shows the total number of orbits of these systems to differ dramatically by more than several millions even for quite low periods all this seems to indicate that surprisingly the total number and the distribution of stable phases is not significantly affected by the specific nature of the nonlinearity present in the equations of motion

an automata theoretic approach to the verification of distributed algorithms abstract we introduce an automata theoretic method for the verification of distributed algorithms running on ring networks in a distributed algorithm an arbitrary number of processes cooperate to achieve a common goal e g elect a leader processes have unique identifiers pids from an infinite totally ordered domain an algorithm proceeds in synchronous rounds which allow processes to exchange pids store them in registers and compare their register contents to specify correctness properties we introduce a logic that can reason about processes and pids we show that model checking distributed algorithms can be reduced to satisfiability in propositional dynamic logic with loop and converse using this reduction we provide an automata theoretic approach to proving distributed algorithms correct up to a given number of rounds overall we show that round bounded verification of distributed algorithms over rings is pspace complete provided the number of rounds is given in unary

on the expressive power of movement and restriction in pure mobile ambients pure mobile ambients is a process calculus suitable to focus on issues related to mobility abstracting away from aspects concerning process communication however it incorporates name restriction i e the vn binder and ambient movement i e the in and out capabilities that can be seen as characteristics adapted or directly borrowed from the tradition of communication based process calculi for this reason we retain that it is worth to investigate whether or not these features can be removed from pure mobile ambients without losing expressive power to this aim we consider two variants of pure mobile ambients which differ in the way infinite processes can be defined the former exploits process replication while the latter is more general and permits recursive process definition we analyse whether or not the elimination of ambient movement and or name restriction reduces the expressive power of these two calculi using the decidability of process termination as a yardstick we prove that name restriction can be removed from both calculi without reducing the expressive power on the other hand the elimination of both ambient movement and name restriction strictly reduces the expressive power of both calculi as far as the elimination of only ambient movement is concerned we prove an interesting discrimination result process termination is undecidable under recursive process definition while it turns out to be decidable under process replication

a capacity scaling heuristic for the multicommodity capacitated network design problem in this paper we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem the capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities which depend on flow volumes on the arcs by combining a column and row generation technique and a strong formulation including forcing constraints this heuristic derives high quality results and computational effort can be reduced considerably the capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem

a new optimization algorithm for the vehicle routing problem with time windows the vehicle routing problem with time windows vrptw is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service in this paper we present the development of a new optimization algorithm for its solution the lp relaxation of the set partitioning formulation of the vrptw is solved by column generation feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming the lp solution obtained generally provides an excellent lower bound that is used in a branch and bound algorithm to solve the integer set partitioning formulation our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark vrptw test problems the algorithm was capable of optimally solving 100 customer problems this problem size is six times larger than any reported to date by other published research

infinite hierarchies of nonlinearly dependent periodic orbits quadratic maps are used to show explicitly that the skeleton of unstable periodic orbits underlying classical and quantum dynamics is stratified into a doubly infinite hierarchy of orbits inherited from a set of basic seeds through certain nonlinear transformations t alpha x the hierarchy contains nonunique substructurings which arise from the different possibilities of sequencing the transformations t alpha x the structuring of the orbital skeleton is shown to be generic for abelian equations i e for all dynamical systems generated by iterating rational functions

a branch and cut and price algorithm for one dimensional stock cutting and two dimensional two stage cutting abstract the one dimensional cutting stock problem 1d csp and the two dimensional two stage guillotine constrained cutting problem 2d 2cp are considered in this paper the gilmore gomory models of these problems have very strong continuous relaxations providing a good bound in an lp based solution approach in recent years there have been several efforts to attack the one dimensional problem by lp based branch and bound with column generation called branch and price and by general purpose c hv a tal g omory cutting planes in this paper we investigate a combination of both approaches i e the lp relaxation at each branch and price node is strengthened by c hv a tal g omory and g omory mixed integer cuts the branching rule is that of branching on variables of the gilmore gomory formulation tests show that for 1d csp general purpose cuts are useful only in exceptional cases however for 2d 2cp their combination with branching is more effective than either approach alone and mostly better than other methods from the literature

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

a structural induction theorem for processes this paper deals with the formal verification of finite state systems that hav an arbitrary number of isomorphic components we present a technique for inductively generalizing tests on a system of fixed size in order to show that a system of arbitrary size satisfies a given specification this makes it possible to use finite state verification systems such as cospan to verify parameterized protocols the method also may be useful for verifying systems of fixed but large size since it reduces the size of the system that must be checked automatically the basis of the method is a structural induction theorem for processes which is stated and proved in this paper the theorem applies to a variety of process formalisms satisfying simple algebraic laws we give examples of proofs using the calculus of communicating systems ccs and the s r model

uniformly stabilizing sets of switching sequences for switched linear systems a set of switching sequences of a discrete time switched linear system is said to be uniformly stabilizing if the system is uniformly exponentially stable over all switching sequences that belong to the set based on the recent result that a switched linear system is uniformly stable if and only if an increasing countable union of linear matrix inequality conditions is satisfied we characterize all uniformly stabilizing sets of switching sequences a discrete time hybrid automaton of the automobile engine is considered to illustrate the result

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

alternating two way ac tree automata we explore the notion of alternating two way tree automata modulo the theory of finitely many associative commutative ac symbols this was prompted by questions arising in cryptographic protocol verification in particular in modeling group key agreement schemes based on diffie hellman like functions where the emptiness question for intersections of such automata is fundamental this also has independent interest we show that the use of general push clauses or of alternation leads to undecidability already in the case of one ac symbol with only functions of arity zero on the other hand emptiness is decidable in the general case of several function symbols including several ac symbols provided push clauses are unconditional and intersection clauses are final this class of automata is also shown to be closed under intersection

crew pairing at air france abstract in the airline industry crew schedules consist of a number of pairings these are round trips originating and terminating at the same crew home base composed of legal work days called duties separated by rest periods the purpose of the airline crew pairing problem is to generate a set of minimal cost crew pairings covering all flight legs the set of pairings must satisfy all the rules in the work convention and all the appropriate air traffic regulations the resulting constraints can affect duty construction may restrict each pairing or be imposed on the overall crew schedule the pairing problem is formulated as an integer nonlinear multi commodity network flow problem with additional resource variables nonlinearities occur in the objective function as well as in a large subset of constraints a branch and bound algorithm based on an extension of the dantzig wolfe decomposition principle is used to solve this model the master problem becomes a set partitioning type model as in the classical formulation while pairings are generated using resource constrained shortest path subproblems this primal approach implicitly considers all feasible pairings and also provides the optimality gap value on a feasible solution a nice feature of this decomposition process is that it isolates all nonlinear aspects of the proposed multi commodity model in the subproblems which are solved by means of a specialized dynamic programming algorithm we present the application and implementation of this approach at air france it is one of the first implementations of an optimal approach for a large airline carrier we have chosen a subproblem network representation where the duties rather than the legs are on the arcs this ensures feasibility relative to duty restrictions by definition as opposed to lavoie minoux and odier 1988 the nonlinear cost function is modeled without approximations the computational experiments were conducted using actual air france medium haul data even if the branch and bound trees were not fully explored in all cases the gaps certify that the computed solutions are within a fraction of one percentage point of the optimality our results illustrate that our approach produced substantial improvements over solutions derived by the expert system in use at air france their magnitude led to the eventual implementation of the approach

dual optimal inequalities for stabilized column generation column generation is one of the most successful approaches for solving large scale linear programming problems however degeneracy difficulties and long tail effects are known to occur as problems become larger in recent years several stabilization techniques of the dual variables have proven to be effective we study the use of two types of dual optimal inequalities to accelerate and stabilize the whole convergence process added to the dual formulation these constraints are satisfied by all or a subset of the dual optimal solutions therefore the optimal objective function value of the augmented dual problem is identical to the original one adding constraints to the dual problem leads to adding columns to the primal problem and feasibility of the solution may be lost we propose two methods for recovering primal feasibility and optimality depending on the type of inequalities that are used our computational experiments on the binary and the classical cutting stock problems and more specifically on the so called triplet instances show that the use of relevant dual information has a tremendous effect on the reduction of the number of column generation iterations

efficient cuts in lagrangean relax and cut schemes abstract lagrangean relaxation produces bounds on the optimal value of mixed integer programming problems these bounds together with integer feasible solution values provide intervals bracketing the optimal value of the original problem when the residual gap i e the relative size of the interval is too large for the approximations to be deemed satisfactory it is desirable to strengthen the lagrangean bounds one possible strengthening technique consists of identifying cuts which are violated by the current lagrangean solution and dualizing them unfortunately not every valid inequality that is currently violated will improve the lagrangean relaxation bound when dualized this paper investigates what makes a violated cut efficient in improving bounds it also provides examples of efficient cuts for several mixed integer programming problems

theory of interaction abstract theory of interaction aims to provide a foundational framework for computation and interaction it proposes four fundamental principles that characterize the common features of all models of computation and interaction these principles suffice to support a model independent treatment of the two most important relationships in computer science the equality between processes and the relative expressiveness between models based on the two relationships the theory of equality the theory of expressiveness and the theory of completeness are developed

a note on a lp based heuristic for a time constrained routing problem in their paper avella et al 2006 investigate a time constrained routing problem the core of the proposed solution approach is a large scale linear program that grows both row and column wise when new variables are introduced thus a column and row generation algorithm is proposed to solve this linear program optimally and an optimality condition is presented to terminate the column and row generation algorithm we demonstrate by using lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination

linearizing well quasi orders and bounding the length of bad sequences we study the length functions of controlled bad sequences over some well quasi orders wqo s and classify them in the fast growing hierarchy we develop a new and self contained study of the length of bad sequences over the disjoint product in n n dickson s lemma which leads to recently discovered upper bounds but through a simpler argument we also give a tight upper bound for the length of controlled decreasing sequences of multisets of n n with the underlying lexicographic ordering and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering with the underlying disjoint product ordering we apply this last result to attain complexity upper bounds for the emptiness problem of itca and atra automata for the case of the product and majoring wqo s the idea is to linearize bad sequences i e to transform a bad sequence over a wqo into a decreasing one over a well order for which upper bounds can be more easily handled

rational subsets and submonoids of wreath products it is shown that membership in rational subsets of wreath products h v with h a finite group and v a virtually free group is decidable on the other hand it is shown that there exists a fixed finitely generated submonoid in the wreath product z z with an undecidable membership problem

algorithmic analysis of programs with well quasi ordered domains over the past few years increasing research effort has been directed towards the automatic verification of infinite state systems this paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability we present decidability results for a class of systems called well structured systems which consist of a finite control part operating on an infinite data domain the results assume that the data domain is equipped with a preorder which is a well quasi ordering such that the transition relation is monotonic a simulation with respect to the preorder we show that the following properties are decidable for well structured systems reachability whether a certain set of control states is reachable other safety properties can be reduced to the reachability problem eventuality whether all executions eventually reach a given set of control states represented as afp in ctl simulation whether there exists a simulation between a finite automaton and a well structured system the simulation problem will be shown to be decidable in both directions we also describe how these general principles subsume several decidability results from the literature about timed automata relational automata petri nets and lossy channel systems

wqo is decidable for factorial languages a language is factorial if it is closed under taking factors i e contiguous subwords every factorial language can be described by an antidictionary i e a minimal set of forbidden factors we show that the problem of deciding whether a factorial language given by a finite antidictionary is well quasi ordered under the factor containment relation can be solved in polynomial time we also discuss possible ways to extend our solution to permutations and graphs

computational study of large scale p median problems given a directed graph g v a the p median problem consists of determining p nodes the median nodes minimizing the total distance from the other nodes of the graph we present a branch and cut and price algorithm yielding provably good solutions for instances with v 3795 key ingredients of the algorithm are a delayed column and row generation technique exploiting the special structure of the formulation to solve the lp relaxation and cutting planes to strengthen the formulation and limit the size of the enumeration tree

blocking in fully connected networks of arbitrary size the problem of checking blocking properties is studied for networks consisting of arbitrary numbers of finite state discrete event subsystems the topology of the networks is that of a fully connected graph any subsystem can potentially interact with any other two types of blocking are studied component blocking whereby a subsystem is potentially prevented from entering its set of marker states and network blocking whereby the subsystems are potentially unable to occupy marker states simultaneously it is shown that if the subsystems are all identical and broadcast actions are permitted both types of blocking properties are undecidable but in the absence of broadcast actions they become decidable if the subsystems are not necessarily identical but only isomorphic then blocking properties are in general undecidable however a template is proposed for ensuring adequate structure for decidability it is claimed that this template is sufficiently general to admit many realistic examples

deciding bisimulation equivalences for a class of non finite state programs traditionally many automatic program verification techniques have been applicable only to finite state programs in this paper we extend some of these techniques to a class of infinite state programs that in addition to having a finite state control component may read store and write but not perform any other computations on data such programs are data independent in the sense that their behavior does not depend on the actual data values supplied we consider the problems of deciding strong equivalence and observation equivalence defined by bisimulations as in ccs between such programs these equivalences have major applications in verification of communication protocols we present reductions of these problems to the problem of deciding strong equivalence and observation equivalence between finite state programs for which polynomial time algorithms exist the equivalence problems on data independent programs are shown to be np hard in the size of the programs

fractal and riddled basins arithmetic signatures in the parameter space of two coupled quadratic maps we investigate the parameter space of two coupledquad ratic logistic maps of special interest is the analytical characterization of the precursors leading to riddled basins we delimit stability domains for orbits with the two lowest periods in addition we study the singularities of the phase space surfaces obtainedby eliminating all parameters from the equations of motion c 2001 elsevier science b v all rights reserved

handling infinitely branching well structured transition systems abstract most decidability results concerning well structured transition systems apply to the finitely branching variant yet some models inserting automata petri nets are naturally infinitely branching here we develop tools to handle infinitely branching wsts by exploiting the crucial property that in the ideal completion of a well quasi ordered set downward closed sets are finite unions of ideals then using these tools we derive decidability results and we delineate the undecidability frontier in the case of the termination the maintainability and the coverability problems coverability and boundedness under new effectiveness conditions are shown decidable

deciding branching time properties for asynchronous programs asynchronous programming is a paradigm that supports asynchronous function calls in addition to synchronous function calls programs in such a setting can be modeled by automata with counters that keep track of the number of pending asynchronous calls for each function as well as a call stack for synchronous recursive computation these programs have the restriction that an asynchronous call is processed only when the call stack is empty the decidability of the control state reachability problem for such systems was recently established in this paper we consider the problems of checking other branching time properties for such systems specifically we consider the following problems termination which asks if there is an infinite non terminating computation exhibited by the system control state maintainability which asks if there is a maximal execution of the system where all the state visited lie in some good set whether the system can be simulated by a given finite state system and whether the system can simulate a given finite state system we present decision algorithms for all these problems

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

plant location with minimum inventory we present an integer programming model for plant location with inventory costs the linear programming relaxation has been solved by dantzig wolfe decomposition in this case the subproblems reduce to the minimum cut problem we have used subgradient optimization to accelerate the convergence of the d w algorithm we present our experience with problems arising in the design of a distribution network for computer spare parts in most cases from a fractional solution we were able to derive integer solutions within 4 of optimality

benders decomposition and column and row generation for solving large scale linear programs with column dependent rows in a recent work muter birbil and bulbul 2013a identified and characterized a general class of linear programming lp problems known as problems with column dependent rows cdr problems these lps feature two sets of constraints with mutually exclusive groups of variables in addition to a set of structural linking constraints in which variables from both groups appear together in a typical cdr problem the number of linking constraints grows very quickly with the number of variables which motivates generating both columns and their associated linking constraints simultaneously on the fly in this paper we expose the decomposable structure of cdr problems via benders decomposition however this approach brings on its own theoretical challenges one group of variables is generated in the benders master problem while the generation of the linking constraints is relegated to the benders subproblem along with the second group of variables a fallout of this separation is that only a partial description of the dual of the benders subproblem is available over the course of the algorithm we demonstrate how the pricing subproblem for the column generation applied to the benders master problem does also update the dual polyhedron and the existing benders cuts in the master problem to ensure convergence ultimately a novel integration of benders cut generation and the simultaneous generation of columns and constraints yields a brand new algorithm for solving large scale cdr problems we illustrate the application of the proposed method on a time constrained routing problem our numerical experiments confirm the outstanding performance of the new decomposition method

reduction and covering of infinite reachability trees abstract we present a structure for transition systems with which the main decidability results on petri nets can be generalized to structured transition systems we define the reduced reachability tree of a structured transition system it allows one to decide the finite reachability tree problem also called the finite termination problem and the finite reachability set problem a general definition of the coverability set is given and the procedure of karp and miller is extended for well structured transition systems we show then that the coverability problem is a decidable problem in the framework of well structured transition systems finally we introduce structured set of terminal states and we show that the finite reachability tree problem and the finite reachability set problem are decidable coverability is an open problem for structured transition systems with a structured set of terminal states

well abstracted transition systems application to fifo automata formal methods based on symbolic representations have been found to be very effective in the case of infinite state systems there has been a great deal of interest in accelerations a technique for characterizing the result of iterating an execution sequence an arbitrary number of times in a sound but not necessarily complete way we propose the use of abstractions as a general framework to design accelerations we investigate semilinear regular expressions slres as symbolic representations for fifo automata in particular we show that a slres are easy to manipulate b slres form the core of known fifo symbolic representations and c slres are sufficient to represent the effect of arbitrary iterations of a loop for fifo automata with one channel

the volume algorithm producing primal solutions with a subgradient method we present an extension to the subgradient algorithm to produce primal as well as dual solutions it can be seen as a fast way to carry out an approximation of dantzig wolfe decomposition this gives a fast method for producing approximations for large scale linear programs it is based on a new theorem in linear programming duality we present successful experience with linear programs coming from set partitioning set covering max cut and plant location

using well structured transition systems to decide divergence for catalytic p systems p systems are a biologically inspired model introduced by gheorghe paun with the aim of representing the structure and the functioning of the cell since their introduction several variants of p systems have been proposed and explored we concentrate on the class of catalytic p systems without priorities associated with the rules we show that the theory of well structured transition systems can be used to decide the divergence problem i e checking for the existence of an infinite computation for such a class of p systems as a corollary we obtain an alternative proof of the nonuniversality of deterministic catalytic p systems an open problem recently solved by ibarra and yen

parallel machine scheduling by column generation parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times if preemption is not allowed then most problems are not only np hard but also very hard from a practical point of view in this paper we show that strong and fast linear programming lower bounds can be computed for an important class of machine scheduling problems with additive objective functions characteristic of these problems is that on each machine the order of the jobs in the relevant part of the schedule is obtained through some priority rule to that end we formulate these parallel machine scheduling problems as a set covering problem with an exponential number of binary variables n covering constraints and a single side constraint we show that the linear programming relaxation can be solved efficiently by column generation because the pricing problem is solvable in pseudo polynomial time we display this approach on the problem of minimizing total weighted completion time on m identical machines our computational results show that the lower bound is singularly strong and that the outcome of the linear program is often integral moreover they show that our branch and bound algorithm that uses the linear programming lower bound outperforms the previously best algorithm

characterizing finite kripke structures in propositional temporal logic abstract we show that if two finite kripke structures can be distinguished by some ctl formula that contains both branching time and linear time operators then the structures can be distinguished by a ctl formula that contains only branching time operators our proof involves showing that for any finite kripke structure m it is possible to construct a ctl formula f m that uniquely characterizes m since one kripke structure may be a trivial unrolling of another we use a notion of equivalence between kripke structures that is similar to the notion of bisimulation studied by milner 15 our first construction of f m requires the use of the nexttime operator we also consider the case in which the nexttime operator is disallowed in ctl formulas the proof in this case requires another notion of equivalence equivalence with respect to stuttering and is much more difficult since it is possible for two inequivalent states to have exactly the same finite behaviors modulo stuttering but different infinite behaviors we also give a polynomial algorithm for determining if two structures are stuttering equivalent and discuss the relevance of our results for temporal logic model checking and synthesis procedures

on the expressiveness of interaction subbisimilarity is proposed as a general tool to classify the relative expressive power of process calculi the expressiveness of several variants of ccs is compared in terms of the subbisimilarity relationship similar investigation is also carried out for the variants of the pi calculus the relative expressiveness of the different forms of the choice operation and the different ways of introducing infinite behaviors are systematically studied in both the frameworks of ccs and pi some issues concerning the expressiveness of both ccs and pi are clarified several open problems are solved along the way the subbisimilarity approach and the relative expressiveness results are applied to show the independence of the operators of the pi calculus the definition of the subbisimilarity relationship can be further strengthened with computational requirement leading to a uniform treatment of computation and interaction

forward analysis and model checking for trace bounded wsts abstract we investigate a subclass of well structured transition systems wsts the trace bounded in the sense of ginsburg and spanier 1964 1 complete deterministic ones which we claim provide an adequate basis for the study of forward analyses as developed by finkel and goubault larrecq 2012 2 indeed we prove that unlike other conditions considered previously for the termination of forward analysis trace boundedness is decidable trace boundedness turns out to be a valuable restriction for wsts verification as we show that it further allows to decide all regular properties on the set of infinite traces of the system

period four stability and multistability domains for the henon map we report the exact analytical expression of the surface w4 a b 0 de ning stability domains for period 4 motions in the h enon map valid for arbitrary eigenvaluesand parameters a and b for 1 fold bifurcations the expression reproduces all previous results and gives a new one for 1 4ip bifurcations it gives analytically the missing boundary needed for the rigorous delimitation of all period 4 stability domains and for the investigation of the arithmetic nature of parameters and trajectories c 2001 elsevier science b v all rights reserved

a dynamic subgradient based branch and bound procedure for set covering we discuss a branch and bound algorithm for set covering whose centerpiece is a new integrated upper bounding lower bounding procedure called dynamic subgradient optimization dynsgrad this new procedure applied to a lagrangean dual at every node of the search tree combines the standard subgradient method with primal and dual heuristics that interact to change the lagrange multipliers and tighten the upper and lower bounds fix variables and periodically restate the lagrangean itself extensive computational testing is reported as a stand alone heuristic dynsgrad performs significantly better than other procedures in terms of the quality of solutions obtainable with a certain computational effort when incorporated into a branch and bound algorithm dynsgrad considerably advances the state of the art in solving set covering problems

a stabilized structured dantzig wolfe decomposition method we discuss an algorithmic scheme which we call the stabilized structured dantzig wolfe decomposition method for solving large scale structured linear programs it can be applied when the subproblem of the standard dantzig wolfe approach admits an alternative master model amenable to column generation other than the standard one in which there is a variable for each of the extreme points and extreme rays of the corresponding polyhedron stabilization is achieved by the same techniques developed for the standard dantzig wolfe approach and it is equally useful to improve the performance as shown by computational results obtained on an application to the multicommodity capacitated network design problem

multiset rewriting for the verification of depth bounded processes with name binding we combine two of the existing approaches to the study of concurrency by means of multiset rewriting multiset rewriting with existential quantification msr and constrained multiset rewriting we obtain n msr where we rewrite multisets of atomic formulae in which terms can only be pure names where some names can be restricted we consider the subclass of depth bounded n msr for which the interdependence of names is bounded we prove that they are strictly well structured transition systems so that coverability termination and boundedness are all decidable for depth bounded n msr this allows us to obtain new verification results for several formalisms with name binding that can be encoded within n msr namely polyadic n pn petri nets with tuples of names as tokens the p calculus msr or mobile ambients

the convex hull of two core capacitated network design problems the network loading problem nlp is a specialized capacitated network design problem in which prescribed point to point demand between various pairs of nodes of a network must be met by installing loading a capacitated facility we can load any number of units of the facility on each of the arcs at a specified arc dependent cost the problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost

a new branch and cut algorithm for the capacitated vehicle routing problem we present a new branch and cut algorithm for the capacitated vehicle routing problem cvrp the algorithm uses a variety of cutting planes including capacity framed capacity generalized capacity strengthened comb multistar partial multistar extended hypotour inequalities and classical gomory mixed integer cuts for each of these classes of inequalities we describe our separation algorithms in detail also we describe the other important ingredients of our branch and cut algorithm such as the branching rules the node selection strategy and the cut pool management computational results for a large number of instances show that the new algorithm is competitive in particular we solve three instances b n50 k8 b n66 k9 and b n78 k10 of augerat to optimality for the first time

a lp based heuristic for a time constrained routing problem abstract in this paper we present a lp based heuristic for the solution of a time constrained routing problem arising from innovative services accessible via world wide web the problem consists of scheduling the visit of a tourist to a given geographical area in order to maximize his satisfaction degree whilst respecting time windows restrictions we refer to this problem as the intelligent tourist problem itp itp is formulated as a set packing problem with side constraints due to the huge number of variables in the formulation the lp relaxation is solved by a column and row generation approach then we run a mip solver over the active columns to get a feasible solution computational experience on real world instances is reported showing the effectiveness of the proposed approach

a lagrangean relax and cut approach for the two stage capacitated facility location problem abstract the two stage capacitated facility location problem is to find the optimal locations of depots to serve customers with a given demand the optimal assignment of customers to depots and the optimal product flow from plants to depots in order to solve this problem a lagrangean heuristic is proposed which is based on the relaxation of the capacity constraints the resulting lagrangean subproblem is an uncapacitated facility location problem with an aggregate capacity constraint and can be solved efficiently by branch and bound methods the best bound available from this relaxation is computed by means of a weighted dantzig wolfe decomposition approach feasible solutions are constructed from those of the lagrangean subproblems by applying simple reassignment procedures furthermore the relaxation is strengthened by adding and dualizing valid inequalities which are violated by the fractional primal solution of the dual master program computational results and comparisons with some other bounds and heuristics for this problem are presented

two variable logic on data trees and xml reasoning motivated by reasoning tasks for xml languages the satisfiability problem of logics on data trees is investigated the nodes of a data tree have a label from a finite set and a data value from a possibly infinite set it is shown that satisfiability for two variable first order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests from this main result decidability of satisfiability and containment for a data aware fragment of xpath and of the implication problem for unary key and inclusion constraints is concluded

a nested decomposition approach to a three stage two dimensional cutting stock problem we consider the cutting of rectangular order pieces into stock pieces of specified width and length the cutting process involves three stages of orthogonal guillotine cutting stock pieces are cut into sections that are cut into slits that are cut into order pieces restrictions imposed on the cutting process make the combinatorial structure of the problem more complex but limit the scope of solution space the objective of the problem is mainly to minimize waste but our model also accounts for other issues such as aging stock pieces urgent or optional orders and fixed setup costs our solution approach involves a nested decomposition of the problem and the recursive use of the column generation technique we use a column generation formulation of the problem gilmore and gomory 1965 and the cutting pattern generation subproblem is itself solved using a column generation algorithm lp based lower bounds on the minimum cost are computed and by rounding the lp solution a feasible solution and associated upper bound is obtained this approach could in principle be used in a branch and bound search to solve the problem to optimality we report computational results for industrial instances the algorithm is being used in industry as a production planning tool

ordinal recursive complexity of unordered data nets abstract data nets are a version of colored petri nets in which tokens carry data from an infinite and linearly ordered domain this is a very expressive class though coverability and termination remain decidable those problems have recently been proven complete for the f class in the fast growing complexity hierarchy we characterize the exact complexity of unordered data nets udn a subclass of data nets with unordered data we bound the length of bad sequences in well quasi orderings of multisets over tuples of naturals by adapting the analogous result by schmitz and schnoebelen for words over a finite alphabet these bounds imply that both problems are in f we prove that this result is tight by constructing udn that weakly compute fast growing functions and their inverses this is the first complete problem for f with an underlying wqo not based on finite words over a finite alphabet

modeling multistage cutting stock problems abstract in multistage cutting stock problems csp the cutting process is distributed over several successive stages every stage except the last one produces intermediate products the list of intermediate products may be given or arbitrary the goal is to minimize the total amount of material taken out of stock to cut finished products sufficient to meet customer demands if the intermediate sizes are given the column generation technique can be applied to multistage cutting problems if the intermediate sizes are not given then another dimension is added to the problem complexity we propose a special procedure for this case that dynamically generates both rows intermediate sizes and columns patterns we refer to this method as row and column generation the method uses an auxiliary problem embedded into the frame of the revised simplex algorithm it is a non linear knapsack problem that can be solved efficiently in contrast to the column generation method the developed technique cannot guarantee the optimal solution however the results of computational experiments are very promising and prove that the method is a valuable addition to the set of tools for modeling and solving multistage csps