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The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.

The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.

This paper examines recent work on the complexity of combinatorial algorithms, highlighting the aims of the work, the mathematical tools used, and the important results. Included are sections discussing ways to measure the complexity of an algorithm, methods for proving that certain problems are very hard to solve, tools useful in the design of good algorithms, and recent improvements in algorithms for solving ten representative problems. The final section suggests some directions for future research. (Author)

The subject of this report is an analysis of the expected, or average case performance of local improvement algorithms. The first chapter presents the basic model, defines the combinatorial structures which are the basis for the analysis, and describes the randomness assumptions upon which the expectation are based. The second chapter examines these structures in more detail, including an analysis of both best and worst case performance. The third chapter discusses simulation results which predict an approximately linear average case performance, and proves an O(n2 log n) upper bound for two of the random distributions assumed. Chapter Four proves some extensions and sharper versions of this upper bound. The fifth chapter applies the model to principal pivoting algorithms for the linear complementarity problem, and to the simplex method. Although local improvement is not guaranteed to find a global optimum for all problems, most notably those that are NP-complete, it is nonetheless often used in these cases. Chapter Six discusses these appllications.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

We consider the homogenized linear feasibility problem, to find an $x$ on the unit sphere, satisfying $n$ line ar inequalities $a_i^Tx\ge 0$. To solve this problem we consider the centers of the insphere of spherical simpl ices, whose facets are determined by a subset of the constraints. As a result we find a new combinatorial algor ithm for the linear feasibility problem. If we allow rescaling this algorithm becomes polynomial. We point out that the algorithm solves as well the more general convex feasibility problem. Moreover numerical experiments s how that the algorithm could be of practical interest.

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Uploaded by zygun

This thesis investigates parallel algorithms for a small, but representative, subclass of graph and matrix problems. In some cases, we develop new algorithms which we analyze for theoretical efficiency. In other cases, we modify and implement existing algorithms which we analyze for practical efficiency. We show how n-node, e-edge graphs can be contracted in a manner similar to the parallel tree contraction algorithm due to Miller and Reif. We give an O((n+e)/lgn)-processor deterministic algorithm that contracts a graph in O(lg squared n) time in the EREW PRAM model.

This thesis investigates parallel algorithms for a small, but representative, subclass of graph and matrix problems. In some cases, we develop new algorithms which we analyze for theoretical efficiency. In other cases, we modify and implement existing algorithms which we analyze for practical efficiency. We show how n-node, e-edge graphs can be contracted in a manner similar to the parallel tree contraction algorithm due to Miller and Reif. We give an O((n+e)/lgn)-processor deterministic algorithm that contracts a graph in O(lg squared n) time in the EREW PRAM model.

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide computationally tractable solution methods even when the dimension of the system and the number of the binary variables are large. The proposed method employs a linear approximation of the objective function such that the approximate problem is defined over the feasible space of the binary decision variables, which is a discrete set. To define such a linear approximation, we propose two different variation methods: one uses continuous relaxation of the discrete space and the other uses convex combinations of the vector field and running payoff. The approximate problem is a 0-1 linear program, which can be solved by existing polynomial-time exact or approximation algorithms, and does not require the solution of the dynamical system. Furthermore, we characterize a sufficient condition ensuring the approximate solution has a provable suboptimality bound. We show that this condition can be interpreted as the concavity of the objective function. The performance and utility of the proposed algorithms are demonstrated with the ON/OFF control problems of interdependent refrigeration systems.

We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud computing, and communicating over a network. This model is quite different from the traditional models, to the extent that neither do the classical equilibrium existence results seem to apply to it nor do any of the efficient algorithmic techniques developed to compute equilibria seem to apply directly. We give a proof of existence of equilibrium and a polynomial time algorithm for finding one, drawing heavily on techniques from LP duality and submodular minimization. We observe that in our market model, the set of equilibrium prices could be a connected, non-convex set. To the best of our knowledge, this is the first natural example of the phenomenon where the set of solutions could have such complicated structure, yet there is a combinatorial polynomial time algorithm to find one. Finally, we show that our model inherits many of the fairness properties of traditional equilibrium models.

We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud computing, and communicating over a network. This model is quite different from the traditional models, to the extent that neither do the classical equilibrium existence results seem to apply to it nor do any of the efficient algorithmic techniques developed to compute equilibria seem to apply directly. We give a proof of existence of equilibrium and a polynomial time algorithm for finding one, drawing heavily on techniques from LP duality and submodular minimization. We observe that in our market model, the set of equilibrium prices could be a connected, non-convex set. To the best of our knowledge, this is the first natural example of the phenomenon where the set of solutions could have such complicated structure, yet there is a combinatorial polynomial time algorithm to find one. Finally, we show that our model inherits many of the fairness properties of traditional equilibrium models.

We consider a generalization of the maximum network flow problem in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e) gamma (e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. We require conservation of flow at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. In this paper we present the first polynomial time combinatorial optimization algorithms for this problem. The algorithms are simple and intuitive.

By now Artificial Intelligence (AI), Theoretical Computer Science (CS theory) and Operations Research (OR) have investigated a variety of search and optimization problems. However, methods from these scientific areas use different problem descriptions, models, and tools. They also address problems with particular efficiency requirements. For example, approaches from CS theory are mainly concerned with the worst-case scenarios and are not focused on empirical performance. A few efforts have tried to apply methods across areas. Usually a significant amount of work is required to make different approaches "talk the same language," be successfully implemented, and, finally, solve the actual same problem with an overall acceptable efficiency. This thesis presents a systematic approach that attempts to advance the state of the art in the transfer of knowledge across the above mentioned areas. In this work we investigate a number of problems that belong to or are close to the intersection of areas of interest of AI, OR and CS theory. We illustrate the advantages of considering knowledge available in different scientific areas and of applying algorithms across distinct disciplines through successful applications of novel hybrid algorithms that utilize benefitial features of known efficient approaches. Testbeds for such applications in this thesis work include both open theoretical problems and ones of significant practical importance. We introduce a representation change that enables us to question the relation between the Pigeonhole Principle and Linear Programming Relaxation. We show that both methods have exactly the same bounding power. Furthermore, even stronger relation appears to be between the two methods: The Pigeonhole Principle is the Dual of Linear Programming Relaxation. Such a relation explains the "hidden magic" of the Pigeonhole Principle, namely its power in establishing upper bounds and its effectiveness in constructing optimal solutions.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

The probability P(alpha, N) that search algorithms for random Satisfiability problems successfully find a solution is studied as a function of the ratio alpha of constraints per variable and the number N of variables. P is shown to be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and exponentially small in N above. The critical behaviour is universal for all algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon) alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to the critical behaviour of random graphs, and the scaling function Phi is exactly calculated through a mapping onto a diffusion-and-death problem.

The probability P(alpha, N) that search algorithms for random Satisfiability problems successfully find a solution is studied as a function of the ratio alpha of constraints per variable and the number N of variables. P is shown to be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and exponentially small in N above. The critical behaviour is universal for all algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon) alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to the critical behaviour of random graphs, and the scaling function Phi is exactly calculated through a mapping onto a diffusion-and-death problem.

In this paper the combinatorial approach for definition of the class size reduction influence on correct recognition probability when one uses 1NN classifier. The recognition results are familiar before database class size reduction for every test object. The probability that recognition system has peculiarity to retain the recognition rate after class size reduction has been determined. The probability definition task that negative recognition results after class size reduction will become positive has also been solved. 

Linear programming is a very general and widely used framework. In this thesis we consider several combinatorial optimization problems that can be viewed as classes of linear programming problems with special structure. It is known that polynomial time algorithms exist for the general linear programming problem. It is not known, however, whether any of them are strongly polynomial. In addition, it seems that the general problem is inherently sequential. For problems with special structure, our goals are to develop sequential and parallel algorithms that are faster than those known for general linear programming and to determine whether strongly polynomial algorithms exist. (1) We develop a technique that extends the classes of problems known to have strongly polynomial algorithms, or known to be quickly solvable in parallel. This technique is used to obtain a fast parallel algorithm and a strongly polynomial algorithm for detecting cycles in periodic graphs of fixed dimension. We mention additional applications to parametric extensions of problems where the number of parameters is fixed. (2) We introduce algorithms for solving linear systems where each inequality involves at most two variables. These algorithms improve over the sequential and parallel running times of previous algorithms. These results are combined with additional ideas to yield faster algorithms for some general network flow problems.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

[CITATION] Solving combinatorial optimization problems by simulated annealing, genetic algorithms, and neural networks Y Lu - 1991 - University of Minnesota Cited by 4

[CITATION] Solving combinatorial optimization problems by simulated annealing, genetic algorithms, and neural networks Y Lu - 1991 - University of Minnesota Cited by 4

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

This project has completed. The PI considered optimization problems with uncertainty in the data. Specifically, algorithms and analysis methods were developed for several optimization scenarios where the random parameters were coming from some unknown probability distribution. One notable result efficiently calculates the average optimal solution for a combinatorial regret problem and provides new bounds for how for this may be from the worst case. For details, see the final report. Further, the project produced 8 published papers and 4 more under review or preparation. The specifics of these references are included in uploaded final report. This work has help to advance the state-of-the-art in robust optimization.

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Deep Boltzmann Machines (DBMs) are generative neural networks with these desired properties. We integrate a DBM into an EDA and evaluate the performance of this system in solving combinatorial optimization problems with a single objective. We compare the results to the Bayesian Optimization Algorithm. The performance of DBM-EDA was superior to BOA for difficult additively decomposable functions, i.e., concatenated deceptive traps of higher order. For most other benchmark problems, DBM-EDA cannot clearly outperform BOA, or other neural network-based EDAs. In particular, it often yields optimal solutions for a subset of the runs (with fewer evaluations than BOA), but is unable to provide reliable convergence to the global optimum competitively. At the same time, the model building process is computationally more expensive than that of other EDAs using probabilistic models from the neural network family, such as DAE-EDA.

We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at most g jobs are active at any given time. The duration for which a machine is active (i.e., "on") is referred to as its active time. The goal is to find a feasible schedule for all jobs, minimizing the total active time. When preemption is allowed at integer time points, we show that a minimal feasible schedule already yields a 3-approximation (and this bound is tight) and we further improve this to a 2-approximation via LP rounding techniques. Our second contribution is for the non-preemptive version of this problem. However, since even asking if a feasible schedule on one machine exists is NP-hard, we allow for an unbounded number of virtual machines, each having capacity of g. This problem is known as the busy time problem in the literature and a 4-approximation is known for this problem. We develop a new combinatorial algorithm that gives a 3-approximation. Furthermore, we consider the preemptive busy time problem, giving a simple and exact greedy algorithm when unbounded parallelism is allowed, i.e., g is unbounded. For arbitrary g, this yields an algorithm that is 2-approximate.

We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization, partition function, base-pair probabilities...) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one to conceptually detach the conformation space/energy model -- captured by the hypergraph model -- from the specific application, assuming unambiguity of the decomposition. To ensure the latter property, we propose a new combinatorial methodology based on generating functions. We extend the set of generic applications by proposing an exact algorithm for extracting generalized moments in weighted distribution, generalizing a prior contribution by Miklos and al. Finally, we illustrate our full-fledged programme on three exemplary conformation spaces (secondary structures, Akutsu's simple type pseudoknots and kissing hairpins). This readily gives sets of algorithms that are either novel or have complexity comparable to classic implementations for minimization and Boltzmann ensemble applications of dynamic programming.

We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization, partition function, base-pair probabilities...) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one to conceptually detach the conformation space/energy model -- captured by the hypergraph model -- from the specific application, assuming unambiguity of the decomposition. To ensure the latter property, we propose a new combinatorial methodology based on generating functions. We extend the set of generic applications by proposing an exact algorithm for extracting generalized moments in weighted distribution, generalizing a prior contribution by Miklos and al. Finally, we illustrate our full-fledged programme on three exemplary conformation spaces (secondary structures, Akutsu's simple type pseudoknots and kissing hairpins). This readily gives sets of algorithms that are either novel or have complexity comparable to classic implementations for minimization and Boltzmann ensemble applications of dynamic programming.

The first methods for tolerating more than a small number of worst- case faults in commonly-Lised networks such as the butterfly, the mesh of trees, and other hypercubic networks. Previously, work on the fault-tolerance properties of these networks was limited to showing how to overcome a single fault by adding an extra stage of hardware to the networks.

Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation algorithms. Our method features the use of approximation-preserving reductions, akin to the notion of parameterized reductions. We exemplify this method to obtain the currently best approximation algorithms for \textsc{Harmless Set}, \textsc{Differential} and \textsc{Multiple Nonblocker}, all of them can be considered in the context of securing networks or information propagation.

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet and Sedgewick with Joyal's species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative Newton method is shown to solve well-founded systems combinatorially. From there, truncations of the corresponding generating series are obtained in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. These results provide important subroutines in random generation. Finally, the approach is extended to combinatorial differential systems.

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet and Sedgewick with Joyal's species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative Newton method is shown to solve well-founded systems combinatorially. From there, truncations of the corresponding generating series are obtained in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. These results provide important subroutines in random generation. Finally, the approach is extended to combinatorial differential systems.

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet and Sedgewick with Joyal's species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative Newton method is shown to solve well-founded systems combinatorially. From there, truncations of the corresponding generating series are obtained in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. These results provide important subroutines in random generation. Finally, the approach is extended to combinatorial differential systems.

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet and Sedgewick with Joyal's species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative Newton method is shown to solve well-founded systems combinatorially. From there, truncations of the corresponding generating series are obtained in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. These results provide important subroutines in random generation. Finally, the approach is extended to combinatorial differential systems.

Addison-Wesley https://archive.org/details/B-001-001-251

This paper is devoted to the solving of graph partition task. We consider five algorithms: iterative, evolutionary, genetic, ant colony and bee colony. A computer program was created during this work. This program realizes the described model of biologically inspired algorithms. Experimental researches have proved efficiency of the bee algorithm in comparison with other algorithms. 

Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available goods and the auctioneer can only accept non-intersecting bids. Since this problem is difficult even to approximate in general, the algorithms are most useful when the bids are restricted to be connected node subsets of an underlying object graph that represents which objects are relevant to each other. The approximation ratios of the algorithms depend on structural properties of this graph and are small constants for many interesting families of object graphs. The running times of the algorithms are linear in the size of the bid graph, which describes the conflicts between bids. Extensions of the algorithms allow for efficient processing of additional constraints, such as budget constraints that associate bids with particular bidders and limit how many bids from a particular bidder can be accepted.

Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available goods and the auctioneer can only accept non-intersecting bids. Since this problem is difficult even to approximate in general, the algorithms are most useful when the bids are restricted to be connected node subsets of an underlying object graph that represents which objects are relevant to each other. The approximation ratios of the algorithms depend on structural properties of this graph and are small constants for many interesting families of object graphs. The running times of the algorithms are linear in the size of the bid graph, which describes the conflicts between bids. Extensions of the algorithms allow for efficient processing of additional constraints, such as budget constraints that associate bids with particular bidders and limit how many bids from a particular bidder can be accepted.

Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available goods and the auctioneer can only accept non-intersecting bids. Since this problem is difficult even to approximate in general, the algorithms are most useful when the bids are restricted to be connected node subsets of an underlying object graph that represents which objects are relevant to each other. The approximation ratios of the algorithms depend on structural properties of this graph and are small constants for many interesting families of object graphs. The running times of the algorithms are linear in the size of the bid graph, which describes the conflicts between bids. Extensions of the algorithms allow for efficient processing of additional constraints, such as budget constraints that associate bids with particular bidders and limit how many bids from a particular bidder can be accepted.

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization problem. Our technique preserves constant factor approximation ratios, as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. Using our technique, we obtain a new 1.61-approximation algorithm for the concave cost facility location problem. For inventory problems, we obtain a new exact algorithm for the economic lot-sizing problem with general concave ordering costs, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs.

We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomial-size fuzzy circuits composed of fuzzy gates. We also introduce fuzzy proof verification systems to model the fuzzification of nondeterminism. Those models help us identify four complexity classes: Fuzzy-FPA of fuzzy functions, Fuzzy-PA and Fuzzy-NPA of fuzzy decision problems, and Fuzzy-NPAO of fuzzy optimization problems. Based on a relative approximation scheme targeting fuzzy membership degree, we formulate two notions of "reducibility" in order to compare the computational complexity of two fuzzy problems. These reducibility notions make it possible to locate the most difficult fuzzy problems in Fuzzy-NPA and in Fuzzy-NPAO.