Exact Algorithm

The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of rectangular bins. The problem is strongly NP-hard and extremely di cult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotical worst-case performance of the continuous lower bound is 1 8 . An exact algorithm for lling a single bin is developed, leading to the de nition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms. Extensive computational results, involving instances with up to 60 boxes, are presented: it is shown that many instances can be solved to optimality within a reasonable time limit.

In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem. We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.

In this paper, we deal with the sequencing and routing problem of order pickers in conventional multiparallel-aisle warehouse systems. For this NP-hard Steiner travelling salesman problem (TSP), exact algorithms only exist for warehouses with at most three cross aisles, while for other warehouse types literature provides a selection of dedicated construction heuristics. We evaluate to what extent reformulating and solving the problem as a classical TSP leads to performance improvements compared to existing dedicated heuristics. We report average savings in route distance of up to 47% when using the LKH (Lin-Kernighan-Helsgaun) TSP heuristic. Additionally, we examine if combining problem-specific solution concepts from dedicated heuristics with high-quality local search features could be useful. Lastly, we verify whether the sophistication of 'state-of-the-art' local search heuristics is necessary for routing order pickers in warehouses, or whether a subset of features suffices to generate high-quality solutions.

While the 1980s were focused on the solution of large sized``easy'' knapsack problems (KPs), this decade has brought several new algorithms, which are able to solve``hard'' large sized instances. We will give an overview of the recent techniques for solving hard KPs, with special emphasis on the addition of cardinality constraints, dynamic programming, and rudimentary divisibility. Computational results, comparing all recent algorithms, are presented.

This paper presents an exact solution framework for solving some variants of the vehicle routing problem (VRP) that can be modeled as set partitioning (SP) problems with additional constraints. The method consists in combining different dual ascent procedures to find a near optimal dual solution of the SP model. Then, a column-and-cut generation algorithm attempts to close the integrality gap left by the dual ascent procedures by adding valid inequalities to the SP formulation. The final dual solution is used to generate a reduced problem containing all optimal integer solutions that is solved by an integer programming solver. In this paper, we describe how this solution framework can be extended to solve different variants of the VRP by tailoring the different bounding procedures to deal with the constraints of the specific variant. We describe how this solution framework has been recently used to derive exact algorithms for a broad class of VRPs such as the capacitated VRP, the VRP with time windows, the pickup and delivery problem with time windows, 123 230 R. Baldacci et al. all types of heterogeneous VRP including the multi depot VRP, and the period VRP. The computational results show that the exact algorithm derived for each of these VRP variants outperforms all other exact methods published so far and can solve several test instances that were previously unsolved.

This paper presents a new exact algorithm for the Capacitated Vehicle Routing Problem (CVRP) based on the set partitioning formulation with additional cuts that correspond to capacity and clique inequalities. The exact algorithm uses a bounding procedure that finds a near optimal dual solution of the LP-relaxation of the resulting mathematical formulation by combining three dual ascent heuristics. The first dual heuristic is based on the q-route relaxation of the set partitioning formulation of the CVRP. The second one combines Lagrangean relaxation, pricing and cut generation. The third attempts to close the duality gap left by the first two procedures using a classical pricing and cut generation technique. The final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between an upper bound and the lower bound achieved. The resulting problem is solved by an integer programming solver. Computational results over the main instances from the literature show the effectiveness of the proposed algorithm.

A partially enumerative algorithm is presented for the maximum clique problem which is very simple to implement. Computational results for an efficient implementation on an IBM 3090 computer are provided for randomly generated graphs with up to 3000 vertices and over one million edges. Also provided are exact specifications for test problems to facilitate future comparisons. In addition, the Fortran 77 code of the proposed algorithm is given. maximum clique * enumerative algorithm * test problems * Fortran program 0167-6377/90/$3.50 © 1990 -Elsevier Science Pubfishers B.V.

The capacitated vehicle routing problem (CVRP) is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. In this paper, we describe a new integer programming formulation for the CVRP based on a two-commodity network flow approach. We present a lower bound derived from the linear programming (LP) relaxation of the new formulation which is improved by adding valid inequalities in a cutting-plane fashion. Moreover, we present a comparison between the new lower bound and lower bounds derived from the LP relaxations of different CVRP formulations proposed in the literature. A new branch-and-cut algorithm for the optimal solution of the CVRP is described. Computational results are reported for a set of test problems derived from the literature and for new randomly generated problems.

The school bus routing problem discussed in this paper, is similar to the standard vehicle routing problem, but has several interesting additional features. In the standard VRP all stops to visit are given. In our school bus routing problem, we assume that a set of potential stops is given, as well as a set of students that can walk to one or more of these potential stops. The school buses used to pick up the students and transport them to their schools have a finite capacity. The goal of this routing problem is to select a subset of stops that will actually be visited by the buses, determine which stop each student should walk to and develop a set of tours that minimize the total distance travelled by all buses. We develop an integer programming formulation for this problem, as well as a problem instance generator. We then show how the problem can be solved using a commercial integer programming solver and discuss some of our results on small instances.

We present a new exact tree-search procedure for solving two-dimensional knapsack problems in which a number of small rectangular pieces, each of a given size and value, are required to be cut from a large rectangular stock plate. The objective is to maximise the value of pieces cut or minimise the wastage. We consider the case where there is a maximum number of times that a piece may be used in a cutting pattern. The algorithm limits the size of the tree search by using a bound derived from a Lagrangean relaxation of a 0-1 integer programming formulation of the problem. Subgradient optimisation is used to optimise this bound. Reduction tests derived from both the original problem and the Lagrangean relaxation produce substantial computational gains. The computational performance of the algorithm indicates that it is an effective procedure capable of solving optimally practical two-dimensional cutting problems of medium size.

The Hierarchical Chinese Postman Problem (HCPP) is a variant of the classical Chinese Postman Problem, in which the arcs are partitioned into clusters and a precedence relation is deÿned on clusters. Practical applications of the HCPP include snow and ice control on the roads and determination of optimal torch paths in ame cutting. The HCPP is NP-hard in general, but polynomial-time solvable if the precedence relation is linear and each cluster is connected. For this case an exact algorithm, requiring a lower computational e ort than previous procedures, is described. and no edge in E i can be traversed before the traversal of all edges in E i−1 is completed. This variant of the HCPP has been used to model some practical problems: the determination of optimal torch paths in ame cutting [10] and snow removal operations in an urban or rural setting where streets are classiÿed according to their importance (generally expressed by the average daily tra c) . Lemieux and Campagna [9] give simple heuristic procedures for a snow plowing problem in which streets are classiÿed into main and secondary streets. Alfa and Liu [1] consider a weaker precedence relation requiring that the traversal of E i starts before the beginning of the traversal of E i+1 and ÿnishes before the ending of the traversal of E i+1 . Dror et al. give a necessary and su cient condition for the existence of a feasible solution and show that the HCPP 0167-6377/00/$ -see front matter c 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 -6 3 7 7 ( 9 9 ) 0 0 0 4 6 -2

Car pooling is a transportation service organized by a large company which encourages its employees to pick up colleagues while driving to/from work to minimize the number of private cars travelling to/from the company site. The car pooling problem consists of defining the subsets of employees that will share each car and the paths the drivers should follow, so that sharing is maximized and the sum of the path costs is minimized. The special case of the car pooling problem where all cars are identical can be modeled as a Dial-a-Ride Problem. In this paper, we propose both an exact and a heuristic method for the car pooling problem, based on two integer programming formulations of the problem. The exact method is based on a bounding procedure that combines three lower bounds derived from different relaxations of the problem. A valid upper bound is obtained by the heuristic method, which transforms the solution of a Lagrangean lower bound into a feasible solution. The computational results show the effectiveness of the proposed methods.

Various deterministic scheduling problems with availability constraints motivated by preventive maintenance attract more and more researchers. Many results involving this constraint have been published in recent years. But there is no recent paper to summarize them. To be convenient for interested researchers, we make this survey. In this paper, complexity results, exact algorithms and approximation algorithms in single machine, parallel machine, flow shop, open shop, job shop scheduling environment with different criteria are surveyed briefly.

In this paper, we propose approximate and exact algorithms for the double constrained two-dimensional guillotine cutting stock problem (DCTDC). The approximate algorithm is a two-stage procedure. The first stage attempts to produce a starting feasible solution to DCTDC by solving a single constrained two dimensional cutting problem, CDTC. If the solution to CTDC is not feasible to DCTDC, the second stage is used to eliminate non-feasibility. The exact algorithm is a branch-and-bound that uses efficient lower and upper bounding schemes. It starts with a lower bound reached by the approximate two-stage algorithm. At each internal node of the branching tree, a tailored upper bound is obtained by solving (relaxed) knapsack problems. To speed up the branch and bound, we implement, in addition to ordered data structures of lists, symmetry, duplicate, and non-feasibility detection strategies which fathom some unnecessary branches. We evaluate the performance of the algorithm on different problem instances which can become benchmark problems for the cutting and packing literature.

Recently hybrid metaheuristics have been design to find solutions for combinatorial optimisation problems. We focus on hybrid procedures that combine local search based metaheuristics with exact algorithms of the operations research field. We present a mapping that outlines the metaheuristic and exact procedures used, the way they are related and the problems they have been applied to.

Container movement by trucks with time constraints at origins and destinations is modeled as an asymmetric ''multi-Traveling Salesmen Problem with Time Windows'' (m-TSPTW) with social constraints. A two-phase exact algorithm based on dynamic programming (DP) is proposed that finds the best routes for a fleet of trucks. Since the m-TSPTW problem is NP-hard, the computational time for optimally solving large size problems becomes prohibitive. For large size problems, we develop a hybrid methodology consisting of DP in conjunction with genetic algorithms. The developed algorithms are compared with an insertion heuristic method. Computational results demonstrate the efficiency of the developed algorithms.

The rapid growth of transactional data brought, soon enough, into attention the need of its further exploitation. In this paper, we investigate the problem of securing sensitive knowledge from being exposed in patterns extracted during association rule mining. Instead of hiding the produced rules directly, we decide to hide the sensitive frequent itemsets that may lead to the production of these rules. As a first step, we introduce the notion of distance between two databases and a measure for quantifying it. By trying to minimize the distance between the original database and its sanitized version (that can safely be released), we propose a novel, exact algorithm for association rule hiding and evaluate it on real world datasets demonstrating its effectiveness towards solving the problem.

In the context of multicriteria decision aid, we address the problem of regrouping alternatives into completely ordered categories based on valued preference degrees. We assume that the number of groups is fixed a priori. This will be referred to as the multicriteria ordered clustering problem. The model is based on the definition of an inconsistency matrix and only uses the ordinal properties of the pairwise preference relations. An exact algorithm is proposed to find the ordered partition and is applied as illustration to the Human Development Index.

The industrial planning has experimented great advances since its beginning for a middle of 20 th century. It has been demonstrated its applications importance into the several industrial where its involved even though the difficult of design exact algorithms that resolved the variants. It has been applied heuristics methods for the planning problems due their high complexity; especially Artificial Intelligence when develop new strategies for resolving one of the most important variant, called task scheduling.

The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of rectangular bins. The problem is strongly NP-hard and extremely di cult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotical worst-case performance of the continuous lower bound is 1 8 . An exact algorithm for lling a single bin is developed, leading to the de nition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms. Extensive computational results, involving instances with up to 60 boxes, are presented: it is shown that many instances can be solved to optimality within a reasonable time limit.

The Heterogeneous Fleet Vehicle Routing Problem is a variant of the classical Vehicle Routing Problem in which customers are served by a heterogeneous fleet of vehicles with various capacities, fixed and variable costs. Due to its complexity, no exact algorithm is known for this problem. This paper describes a genetic algorithm hybridized with two known heuristic methods for this problem. Hybrid genetic algorithms are often referred as memetic algorithms. Computational experiments presenting the performance of the proposed algorithm concerning quality of solution and processing time are reported. On a set of benchmark instances, it produces high-quality solutions, including several new best-known solutions.

An exact algorithm is provided for finding the least median of squares (LMS) line for a bivariate regression with no intercept term. It is shown that the popular Program for RObust reGRES-Sion (PROGRESS) routine will not, in general, find the LMS slope when the intercept is suppressed. A Microsoft Excel workbook that provides the code in Visual Basic is made available at

The Generalized Vehicle Routing Problem (GVRP) is the problem of designing optimal delivery or collection routes, subject to capacity restrictions, from a given depot to a number of prede®ned, mutually exclusive and exhaustive clusters. In this paper we describe an ecient transformation of the GVRP into a Capacitated Arc Routing Problem (CARP) for which an exact algorithm and several approximate procedures are reported in literature. It constitutes the only known approach for solving the GVRP. Ó

In this paper, we describe a new integer programming formulation for the Traveling Salesman Problem with mixed Deliveries and Collections (TSPDC) based on a two-commodity network flow approach. We present new lower bounds that are derived from the linear relaxation of the new formulation by adding valid inequalities, in a cutting-plane fashion. The resulting lower bounds are embedded in a branch-and-cut algorithm for the optimal solution of the TSPDC. Computational results on different classes of test problems taken from the literature indicate the effectiveness of the proposed method.

In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. The problem has several applications in telecommunications network design and in rapid transit systems planning. It is an extension of the classical location–allocation problem introduced in the early 1960s, and closely related versions have been recently studied by several authors. This article formulates the problem as a mixed-integer linear program and strengthens it with the introduction of several families of valid inequalities. These inequalities are shown to be facet-defining and are used to develop a branch-and-cut algorithm. Computational results show that instances involving up to 300 vertices can be solved optimally using the proposed methodology. © 2004 Wiley Periodicals, Inc.

This research is motivated by issues faced by a large manufacturer of semiconductor devices. Semiconductor manufacturing companies allocate millions of dollars every year for new types of machine tools for their facilities. Typically these are special purpose machine tools which are made to order. The rate of change in products and technology makes it dicult for manufacturers to have a good estimate of future tool requirements. Further, manufacturers experience a long lead time while procuring these tools. In this paper, we model the tool capacity planning problem under uncertainty in demand. The number of tools required in a facility is suciently large (nearly hundred or more tools) to make it nearly impossible to obtain ecient exact algorithms. We provide heuristics to ®nd ecient tool procurement plans and test their quality using lower bounds on the formulation. Ó

This paper describes recent research and theoretical results obtained for cement-based materials using computational materials science techniques. Computer-generated microstructure models are used to simulate the microstructure development during hydration, and exact algorithms are applied to these models to compute experimentally verifiable physical properties. Good agreement is found between experimental and simulation results.

In calculating the solvation energy of proteins, the hydration effects, drug binding, molecular docking, etc., it is important to have an efficient and exact algorithms for computing the solvent accessible surface area and the excluded volume of macromolecules. Here we present a Fortran package based on the new exact analytical methods for computing volume and surface area of overlapping spheres. In the considered procedure the surface area and volume are expressed as surface integrals of the second kind over the closed region. Using the stereographic projection the surface integrals are transformed to a sum of double integrals which are reduced to the curve integrals. MPI Fortran version is described as well. The package is also useful for computing the percolation probability of continuum percolation models.

The Generalized Vehicle Routing Problem (GVRP) is the problem of designing optimal delivery or collection routes, subject to capacity restrictions, from a given depot to a number of prede®ned, mutually exclusive and exhaustive clusters. In this paper we describe an ecient transformation of the GVRP into a Capacitated Arc Routing Problem (CARP) for which an exact algorithm and several approximate procedures are reported in literature. It constitutes the only known approach for solving the GVRP. Ó

Bispectral index (BIS) integrates various electroencephalographic (EEG) parameters into a single variable. However, the exact algorithm used to synthesize the parameters to BIS values is not known. The relationship between BIS and EEG parameters was evaluated during nitrous oxide/isoflurane anesthesia. Twenty patients scheduled for elective ophthalmic surgery were enrolled in the study. After EEG recording with a BIS monitor (A-1050) was begun, general anesthesia was induced and maintained with 0.5%-2% isoflurane and 66% nitrous oxide. Using software we developed, we continuously recorded BIS, spectral edge frequency 95% (SEF95), and EEG parameters such as relative beta ratio (BetaRatio), relative synchrony of fast and slow wave (SynchFastSlow), and burst suppression ratio. BetaRatio was linearly correlated with BIS (r ϭ 0.90; P Ͻ 0.01; n ϭ 253) at BIS more than 60. At a BIS range of 30 to 80, SynchFastSlow (r ϭ 0.60; P Ͻ 0.01; n ϭ 3314) and SEF95 (r ϭ 0.75; P Ͻ 0.01; n ϭ 3339) were linearly correlated with BIS. The correlation between BIS and SEF95 was significantly better than the correlation between BIS and SynchFastSlow (P Ͻ 0.01). At BIS less than 30, the burst suppression ratio was inversely linearly correlated with BIS (r ϭ 0.76; P Ͻ 0.01; n ϭ 65). At BIS less than 80, burst-compensated SEF95 was linearly correlated with BIS (r ϭ 0.78; P Ͻ 0.01; n ϭ 3404). In the range of BIS from 60 to 100, BIS can be calculated from Beta-Ratio. At surgical levels of anesthesia, BIS and Synch-FastSlow (a parameter derived from bispectral analysis) or burst-compensated SEF95 (derived from power spectral analysis) are well correlated. However, our results show that SynchFastSlow has no advantage over SEF95 in calculation of BIS.

In this paper we present an exact algorithm for the Windy General Routing Problem. This problem generalizes many important Arc Routing Problems and also has some interesting real-life applications. The Branch & Cut method presented here is based on a cutting-plane algorithm that identifles violated inequalities of several classes of facet-inducing inequalities for the corresponding polyhedron. The whole procedure has

Given an undirected graph G = (V , E), the Vertex Coloring Problem (VCP) requires to assign a color to each vertex in such a way that colors on adjacent vertices are different and the number of colors used is minimized. In this paper, we present an exact algorithm for the solution of VCP based on the well-known Set Covering formulation of the problem. We propose a Branch-and-Price algorithm embedding an effective heuristic from the literature and some methods for the solution of the slave problem, as well as two alternative branching schemes. Computational experiments on instances from the literature show the effectiveness of the algorithm, which is able to solve, for the first time to proven optimality, five of the benchmark instances in the literature, and reduce the optimality gap of many others.

5 Comparison of various VRP relaxations 6 Branch-and-cut methods Separation algorithms Branching strategies 7 Branch-and-cut-and-price method R. Baldacci (DEIS) Exact Algorithms for the VRP May 12, 2008 2 / 66 Outline (2) Pricing and cut generation 8 Set partitioning with additional cuts Finding an optimal VRP solution Bounding procedure Route generation algorithm 9 Summary of the computational experiments 10 Appendix 11 References R. Baldacci (DEIS) Exact Algorithms for the VRP May 12, 2008 3 / 66 Problem description

We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst case time complexity O(c √ n ), where c is some fixed constant that does not depend on the instance. Furthermore, we show that under the exponential time hypothesis, the time complexity cannot be improved to O(c o( √ n) ).

In this paper, we develop a new version of the algorithm proposed in Hi® (Computers and Operations Research 24/8 (1997) 727±736) for solving exactly some variants of (un)weighted constrained twodimensional cutting stock problems. Performance of branch-and-bound procedure depends highly on particular implementation of that algorithm. Programs of this kind are often accelerated drastically by employing sophisticated techniques. In the new version of the algorithm, we start by enhancing the initial lower bound to limit initially the space search. This initial lower bound has already been used in (Journal of the Operational Research Society, 49, 1270±1277), as a heuristic for solving the constrained and unconstrained cutting stock problems. Also, we try to improve the upper bound at each internal node of the developed tree, by applying some simple and ecient combinations. Finally, we introduce some new symmetric-strategies used for neglecting some unnecessary duplicate patterns. The performance of our algorithm is evaluated on some problem instances of the literature and other hard-randomly generated problem instances. 7 (M. Hi®). J (NV-pattern but not a NH-pattern) horizontal combination of the patterns A and

In this paper we consider the problem in which a fleet of M vehicles stationed at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. This problem is referred as the Capacitated Vehicle Routing Problem (CVRP). We present an exact algorithm for solving the CVRP based on a Set Partitioning formulation of the problem. We describe a procedure for computing a valid lower bound to the cost of the optimal CVRP solution that finds a feasible solution of the dual of the LP-relaxation of the set partitioning formulation without generating the entire set partitioning matrix. The dual solution obtained is then used to limit the set of the feasible routes containing the optimal CVRP solutions. The resulting Set Partitioning problem is solved by using a branch and bound algorithm. Computational results are presented for a number of problems derived from the literature. The results show the effectiveness of the proposed method in solving problems up to about 100 customers.

For more than 40 years Branch & Reduce exponential-time backtracking algorithms have been among the most common tools used for finding exact solutions of NP-hard problems. Despite that, the way to analyze such recursive algorithms is still far from producing tight worst-case running time bounds. Motivated by this we use an approach, that we call "Measure & Conquer", as an attempt to step beyond such limitations. The approach is based on the careful design of a non-standard measure of the subproblem size; this measure is then used to lower bound the progress made by the algorithm at each branching step. The idea is that a smarter measure may capture behaviors of the algorithm that a standard measure might not be able to exploit, and hence lead to a significantly better worst-case time analysis.

In this paper, we optimally solve the disjunctively constrained knapsack problem (DCKP), which is a variant of the standard knapsack problem with special disjunctive constraints. First, we develop a generic exact approach which can be considered as a three-phase procedure. The first phase tries to estimate a starting lower bound. The second phase applies a reduction procedure, combined with the lower bound, in order to fix some decision variables to the optimum. The third phase uses an exact branch and bound algorithm that identifies the optimal values of the free decision variables. Second, we design a specialized exact algorithm based upon a dichotomous search combined with a reduction procedure. Third and last, we propose a modified dichotomous search version which is based upon constructing an equivalent model to the DCKP, adding some dominating constraints, and injecting the so-called covering cut. We evaluate the performance of all versions of the algorithm and compare the obtained results to those of other exact algorithms of the literature. Encouraging results have been obtained. ᭧

A company frequently decides on location and design for new facilities in a sequential way. However, for a fixed number of new facilities (in this study we restrict ourselves to the case of two new facilities), the company might improve its profit by taking its decisions for all the facilities simultaneously. In this paper a profit maximization problem is considered, where the market share captured by each facility depends on both the distance to the customers (location) and its quality (design), and it is determined by a Huff-like model. Recent research on this type of models was aimed at finding global optima for a single new facility, holding quality fixed or variable, but no exact algorithm has been proposed to find optimal solutions for more than one facility. The existing algorithms coping with the simultaneous problem do a cycle search in which only one location is optimized independently, holding all other locations fixed; therefore it cannot guarantee that an optimal solution has been found. In this paper we propose an exact interval branch-and-bound algorithm to solve the simultaneous location and design 2-facilities problem. We present some computational results to compare the locations and qualities of the optimal solutions obtained by a sequential and two simultaneous approaches.

Multicut is a fundamental network communication and connectivity problem. It is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NP-completeness and (fixedparameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.

We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean Networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F , and a target time, t, our algorithm automatically finds a sequence of control signals that deterministically drives the BN from I to F at, or before time t, or else guarantees that no such policy exists. Despite recent hardness-results for finding control policies for BNs, we show that, in practice, our algorithm runs in seconds to minutes on over 13,400 BNs of varying sizes and topologies, including a BN model of embryogenesis in Drosophila melanogaster with 15,360 Boolean variables. We then extend our method to automatically identify a set of Boolean transfer functions that reproduce the qualitative behavior of gene regulatory networks. Specifically, we automatically learn a BN model of D. melanogaster embryogenesis in 5.3 seconds, from a space containing 6.9 × 10 10 possible models.

This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N 9 to N 6 . The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N 3 . In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N 4 , while the previously proposed algorithm is of order N 6 . The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.

We consider the following problem of scheduling with conflicts (SWC): Find a minimum makespan schedule on identical machines where conflicting jobs cannot be scheduled concurrently. We study the problem when conflicts between jobs are modeled by general graphs.

Garantir les performances d'un service à travers le réseau de plusieurs opérateurs est un problème complexe. Ce problème nécessite le calcul de chemins qui traversent plusieurs domaines et qui répondent aux différentes contraintes de qualité de service. De plus, les méthodes de calcul utilisées doivent respecter les contraintes de confidentialité et d'autonomie imposés par les domaines de différents opérateurs. Afin d'améliorer le temps de réponse, les opérateurs de réseaux mettent en place le pré-calcul de chemins. Le pré-calcul consiste à préparer à l'avance des chemins ou des segments de chemins qui sont utilisés ultérieurement dans le calcul de chemins de bout en bout. Dans ce travail, nous étudions le problème du pré-calcul de chemins inter-domaines soumis à plusieurs contraintes de qualité de service. Nous proposons une architecture qui met en place les solutions de précalcul inter-domaine et introduisons deux nouveaux algorithmes de pré-calcul ID-PPPA et ID-ME...

Let A and B be two sets of n objects in R d , and let Match be a (one-to-one) matching between A and B. Let min(Match), max(Match), and Σ(Match) denote the length of the shortest edge, the length of the longest edge, and the sum of the lengths of the edges of Match respectively. Bottleneck matching-a matching that minimizes max(Match)-is suggested as a convenient way for measuring the resemblance between A and B. Several algorithms for computing, as well as approximating, this resemblance are proposed. The running time of all the algorithms involving planar objects is roughly O(n 1.5 ). For instance, if the objects are points in the plane, the running time of the exact algorithm is O(n 1.5 log n). A semi-dynamic data-structure for answering containment problems for a set of congruent disks in the plane is developed. This data structure may be of independent interest.

A new transistor sizing algorithm, SEA (Simple Exact Algorithm), for optimizing low-power and high-speed arithmetic integrated circuits is proposed. In comparison with other transistor sizing algorithms, simplicity, accuracy, independency of order and initial sizing factors of transistors, and flexibility in choosing the optimization parameters such as power consumption, delay, Power-Delay Product (PDP), chip area or the combination of them are considered as the advantages of this new algorithm. More exhaustive rules of grouping transistors are the main trait of our algorithm. Hence, the SEA algorithm dominates some major transistor sizing metrics such as optimization rate, simulation speed, and reliability. According to approximate comparison of the SEA algorithm with MDE and ADC for a number of conventional full adder circuits, delay and PDP have been improved 55.01% and 57.92% on an average, respectively. By comparing the SEA and Chang's algorithm, 25.64% improvement in PDP and 33.16% improvement in delay have been achieved. All the simulations have been performed with 0.13 μm technology based on the BSIM3v3 model using HSpice simulator software.

This research is motivated by issues faced by a large manufacturer of semiconductor devices. Semiconductor manufacturing companies allocate millions of dollars every year for new types of machine tools for their facilities. Typically these are special purpose machine tools which are made to order. The rate of change in products and technology makes it diÅcult for manufacturers to have a