Exact Algorithm

The Quadratic Assignment Problem is known as a combinatorial optimization problem, which is very hard to solve exactly. A survey of recent methods for solving this problem is given. Then an exact algorithm is presented along with computational results on a variety of test problems. This algorithm obtains very good results and, for the first time to our knowledge, solves exactly problems of size up to twenty, this in less than twenty minutes.

The new family of Field Programmable Gate Arrays, CLI6000 from Concurrent Logic Inc realizes the truly Cellular Logic. It has been mainly designed for the realization of data path architectures. However, introduced by it new universal logic cell calls also for new logic synthesis methods based o n r egularity of connections. In this paper we present two programs, exact and approximate, for the minimization of Permuted R eed-Muller Trees that are obtained b y r epetitive application of Davio expansions (Shannon expansions for EXOR gates) in all possible orders of variables in subtrees. Such trees are p articularly well matched t o b oth the realization of logic cell and connection structure of the CLI6000 device. It is shown on several standard b enchmarks that the heuristic algorithm gives good quality results in much less time than the exact algorithm.

We propose a new nonparametric classification framework for numerical patterns, which can also be exploitable for exploratory data analysis. The key idea is approximating each class region by a family of convex geometric sets which can cover samples of the target class without containing any samples of other classes. According to this framework, we consider a combinatorial classifier based on a family of spheres, each of which is the minimum covering sphere for a subset of positive samples and does not contain any negative samples. We also present a polynomial-time exact algorithm and an incremental randomized algorithm to compute it. In addition, we discuss the soft-classification version and evaluate these algorithms by some numerical experiments.

In this research we study the multi-product economic lot scheduling problem (ELSP) with manufacturing and remanufacturing opportunities. Manufacturing and remanufacturing operations are performed on the same production line. Both manufactured and remanufactured products have the same quality thus fulfil the same demand stream. firstly studied this type of economic lot scheduling problem with returns (ELSPR) and presented a complex algorithm for the optimal solution. More recently Teunter et al (2009) proposed several heuristics to deal with the same problem using more computational efficient approaches. However, both studies have limited the attention to the common cycle policy with the assumption that single (re)manufacturing lot is used for each item in each cycle. Relaxing the constraint of common cycle time and a single (re)manufacturing lot for each item in each cycle, we propose a simple, easy to implement algorithm, based on Segerstedt (1999), to solve the model using a basic period policy. Several numerical examples show the applicability of the algorithm and the cost savings.

We provide parameterized algorithms for nonblocker, the parametric dual of the well known dominating set problem. We exemplify three methodologies for deriving parameterized algorithms that can be used in other circumstances as well, including the (i) use of extremal combinatorics (known results from graph theory) in order to obtain very small kernels, (ii) use of known exact algorithms for the (nonparameterized) minimum dominating set problem, and (iii) use of exponential space. Parameterized by the size k d of the non-blocking set, we obtain an algorithm that runs in time O * (2.5154 k d ). We also discuss planar and bipartite special graph classes.

We establish a refined search tree technique for the parameterized DOMINATING SET problem on planar graphs. Here, we are given an undirected graph and we ask for a set of at most k vertices such that every other vertex has at least one neighbor in this set. We describe algorithms with running times O(8 k n) and O(8 k k + n 3 ), where n is the number of vertices in the graph, based on bounded search trees. We describe a set of polynomial time data-reduction rules for a more general "annotated" problem on black/white graphs that asks for a set of k vertices (black or white)

In this paper we discuss the complexity and approximability of the minimum corridor connection problem where, given a rectilinear decomposition of a rectilinear polygon into "rooms", one has to find the minimum length tree along the edges of the decomposition such that every room is incident to a vertex of the tree. We show that the problem is strongly NP-hard and give an subexponential time exact algorithm. For the special case of k-outerplanar graphs the running time becomes O(n 3 ). We develop a polynomial time approximation scheme for the case when all rooms are fat and have nearly the same size. When rooms are fat but are of varying size we give a polynomial time constant factor approximation algorithm.

During the past few years, there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior. This extension involves both modeling and computational challenges. One way to describe choice behavior is to assume that each customer belongs to a segment, which is characterized by a consideration set, i.e., a subset of the products provided by the firm that a customer views as options. Customers choose a particular product according to a multinomial-logit criterion, a model widely used in the marketing literature. In this paper, we consider the choice-based, deterministic, linear programming model (CDLP) of Gallego et al. (2004) [Gallego, G., G. Iyengar, R. Phillips, A. Dubey. 2004. Managing flexible products on a network. Technical Report CORC TR-2004-01, Department of Industrial Engineering and Operations Research, Columbia University, New York], and the follow-up dynamic programming decompositi...

A variety of hybrids of Constraint Programming, Artificial Intelligence and Operations Research techniques have given impressive results. Three recent approaches are (i) the use of relaxations in constraint systems, (ii) non-systematic backtracking to boost the scalability of constraint solvers, and (iii) non-systematic backtracking to boost the scalability of branch-and-bound search. This paper describes a hybrid of all three approaches that combines non-systematic backtracking, SAT-based inference and linear relaxation. It is intended for large MIPs that are hard for reasons of both optimisation and feasibility. Such problems are of practical as well as theoretical interest and we expect the hybrid to find many applications. It is currently under development and results will be reported at the workshop.

The k-means problem is one of the most popular models in cluster analysis that minimizes the sum of the squared distances from clustered objects to the sought cluster centers (centroids). The simplicity of its algorithmic implementation encourages researchers to apply it in a variety of engineering and scientific branches. Nevertheless, the problem is proven to be NP-hard which makes exact algorithms inapplicable for large scale problems, and the simplest and most popular algorithms result in very poor values of the squared distances sum. If a problem must be solved within a limited time with the maximum accuracy, which would be difficult to improve using known methods without increasing computational costs, the variable neighborhood search (VNS) algorithms, which search in randomized neighborhoods formed by the application of greedy agglomerative procedures, are competitive. In this article, we investigate the influence of the most important parameter of such neighborhoods on the c...

We present exact algorithms for finding a solution to the twodimensionaltranslational containment problem: find translationsfor k polygons which place them inside a polygonalcontainer without overlapping. We also give an approximatealgorithm: given any ffl, it finds a set of translations such thatno point of any polygon is more than 2ffl inside the boundaryof any other polygon or outside the container.The term

We present a continuous, bilinear formulation for the fixed charge network flow problem. This formulation is used to derive an exact algorithm for the fixed charge network flow problem converging in a finite number of steps. Some preliminary computational experiments are reported to show the performance of the algorithm.

In this paper we apply a heuristic method based on artificial neural networks (NN) in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz meanvariance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the NN heuristic and we compare them to those obtained with three previous heuristic methods. The portfolio selection problem is an instance from the family of quadratic programming problems when the standard Markowitz mean-variance model is considered. But if this model is generalized to include cardinality and bounding constraints, then the portfolio selection problem becomes a mixed quadratic and integer programming problem. When considering the latter model, there is not any exact algorithm able to solve the portfolio selection problem in an efficient way. The use of heuristic algorithms in this case is imperative. In the past some heuristic methods based mainly on evolutionary algorithms, tabu search and simulated annealing have been developed. The purpose of this paper is to consider a particular neural network (NN) model, the Hopfield network, which has been used to solve some other optimisation problems and apply it here to the portfolio selection problem, comparing the new results to those obtained with previous heuristic algorithms.

We present an algorithm to implement "most balancing" packet scheduling policies in a discrete-time multi-server system of parallel queues with independent random queue-server connectivity. The MB policies are characterized by minimizing the total difference in queue lengths at every time slot. The proposed algorithm produces the server allocation strategy that achieves the minimum "imbalance index" at every time slot. This algorithm has a reduced computational complexity compared to a full-search through the set of all feasible policies. We also provide a low-complexity approximate implementation algorithm that performs close to the exact algorithm. Simulation results confirm our claims.

The MAP problem for Bayesian networks is the problem of finding for a set of variables an instantiation of highest posterior probability given the available evidence. The problem is known to be computationally infeasible in general. In this paper, we present a method for preprocessing the MAP problem with the aim of reducing the runtime requirements for its solution. Our method exploits the concepts of Markov and MAP blanket for deriving partial information about a solution to the problem. We investigate the practicability of our preprocessing method in combination with an exact algorithm for solving the MAP problem for some real Bayesian networks.

We introduce a formal model of cost-sensitive fault remediation, derive an exact algorithm for solving the special case of deterministic observations, and demonstrate it on two example problems. This effort is part of two self-healing software projects that attempt to use collected data for better decision making in emerging autonomic systems.

The vehicle routing problem with backhauls (VRPB) as an extension of the classical vehicle routing problem (VRP) attempts to define a set of routes which services both linehaul customers whom product are to be delivered and backhaul customers whom goods need to be collected. A primary objective for the problem usually is minimizing the total distribution cost. Most real-life problems have other objectives addition to this common primary objective. This paper describes a multi-objective model for VRPB with time windows (VRPBTW) and some new assumptions. We present a goal programming approach and a heuristic algorithm to solve the problem. Computational experiments are carried out and performance of developed methods is discussed.

We consider the problem of weighted rectilinear approximation on the plane and offer both exact algorithms and heuristics with provable performance bounds. Let S = {(p i , w i)} be a set of n points pi in the plane, with associated distance-modifying weights wi > 0. We present algorithms for finding the best fit to S among x-monotone rectilinear polylines R with a given number k < n of horizontal segments. We measure the quality of the fit by the greatest weighted vertical distance, i.e., the approximation error is max 1≤i≤n w i d v (p i , R), where d v (p i , R) is the vertical distance from pi to R. We can solve for arbitrary k optimally in O(n 2) or approximately in O(n log 2 n) time. We also describe a randomized algorithm with an O(n log 2 n) expected running time for the unweighted case and describe how to modify it to handle the weighted case in O(n log 3 n) expected time. All algorithms require O(n) space.

We consider the problem of weighted rectilinear approximation on the plane and offer both exact algorithms and heuristics with provable performance bounds. Let S = {(p i , w i)} be a set of n points pi in the plane, with associated distance-modifying weights wi > 0. We present algorithms for finding the best fit to S among x-monotone rectilinear polylines R with a given number k < n of horizontal segments. We measure the quality of the fit by the greatest weighted vertical distance, i.e., the approximation error is max 1≤i≤n w i d v (p i , R), where d v (p i , R) is the vertical distance from pi to R. We can solve for arbitrary k optimally in O(n 2) or approximately in O(n log 2 n) time. We also describe a randomized algorithm with an O(n log 2 n) expected running time for the unweighted case and describe how to modify it to handle the weighted case in O(n log 3 n) expected time. All algorithms require O(n) space.

We exploit the "regularity" of Boolean functions with the purpose of decreasing the time for constructing minimal threelevel expressions, in the sum of pseudoproducts (SPP) form recently developed. The regularity of a Boolean function of variables can be expressed by an autosymmetry degree (with 0). = 0 means no regularity, that is we are not able to provide any advantage over standard synthesis. For 1 the function is said to be autosymmetric, and a new function depending on variables only, called the restriction of , is identified in time polynomial in the number of points of. The relation between and is discussed in depth to show how a minimal SPP form for can be build in linear time from a minimal SPP form for. The concept of autosymmetry is then extended to functions with don't care conditions, and the SPP minimization technique is duly extended to such functions. A large set of experimental results is presented, showing that 61% of the outputs for the functions in the classical ESPRESSO benchmark suite are autosymmetric. The minimization time for such functions is critically reduced, and cases otherwise intractable are solved. The quality of the corresponding circuits, measured with some well established cost functions, is also improved. Finally, we discuss the role and meaning of autosymmetric functions, and why a great amount of functions of practical interest fall in this class.

We introduce an exact algorithm for maximizing the number of satisfied constraints in an overconstrained CSP (Max-CSP). The algorithm, which can also solve weighted CSP, probabilistic CSP and other similar problems, is based on directed arc-inconsistency counts (DAC). The usage of DAC increases the lower bound of branch and bound based algorithms for Max-CSP, improving their efficiency. Originally, DAC were defined following a static variable ordering. In this paper, we relax this condition, showing how DAC can be defined from a directed constraint graph. These new graph-based DAC can be effectively used for lower bound computation. Interestingly, any directed constraint graph of the considered problem is suitable for DAC computation, so the selected graph can change dynamically during search, aiming at optimizing the exploitation of directed arcinconsistencies. In addition, directed arc-inconsistencies are maintained during search, propagating the effect of value pruning. With these new elements we present the PFC maintaining reversible DAC algorithm (PFC-MRDAC), a natural successor of PFC-DAC for Max-CSP. We provide experimental evidence for the superiority of PFC-MRDAC on random and real overconstrained CSP instances, including problems with weighted constraints.

A binary matrix A is said to have the "Consecutive Ones Property" (C1P) if its columns can be permuted so that in each row, the ones appear in one run (i.e., all ones are adjacent). The Consecutive Ones Submatrix (COS) problem is, given a binary matrix A and a positive integer m 0 , to find m 0 columns of A that form a submatrix with the C1P property. The matrix reordering problem is to find a matrix A obtained by permuting the columns of A that minimizes C r (A) the number of sequences of consecutive ones in A. In this paper, by using two quadratic forms, we calculate the number C r (A). We apply the obtained results to the orthogonal matrices and Hamming matrices, in addition, the two above problems can be solved for these matrices.

After this column I am resigning as SIGACT News Book Review Editor. I’ve been editing this column for 17 years which is longer than anyone should have a job of this type. I have enjoyed editing this column and reviewing books. I have enjoyed getting to know publishers and authors and reviewers. I have enjoyed getting books in the mail that I want to read. I have not enjoyed giving those books to others who really will read them. I want to thank all authors-of-books, authors-of-reviews, publishers, and readers-of-this-column. The first three mentioned were crucial to getting this column published. The fourth mentioned are why we get this column published. Fred Green will be taking over starting with the next issue. If you want to review any of the books in the Books we want reviewed list then email both him [email protected] and me [email protected].

Cancer screening is a method of preventing cancer by early detecting and treating abnormalities. One of the most critical screening phase is invitation planning since screening resources are limited and there are many people to invite. For this reason, smart resource allocation approaches are needed. In the paper, we propose and compare two solutions for smart invitation plan definition, one based on greedy approaches and one based on Constraint Programming techniques that enable the definition of the optimal invitation plan.

In hard real-time systems timeliness is as important as functional correctness. Such systems contain so called hard real-time tasks (HRT tasks) which must be finished by a given deadline. One of the methods of scheduling of HRT tasks is periodic loading introduced by Schweitzer, Dror, and Trudeau. The paper presents an extension to that method which allows for deterministic utilization of cache memory in hard real-time systems. It is based on a new version of the Knapsack problem named Knapsack-Lightening. In the paper the Knapsack-Lightening problem is defined, its complexity is analyzed, and an exact algorithm along with two heuristics are presented. Moreover the application of the Knapsack-Lightening problem to scheduling HRT tasks is described.

The Minimum Vertex Cover (MVC) problem is a well known combinatorial optimization problem of great importance in theory and applications. In recent years, local search has been shown to be an effective and promising approach to solve hard problems, such as MVC. In this paper, we introduce two new local search algorithms for MVC, called EWLS (Edge Weighting Local Search) and EWCC (Edge Weighting Configuration Checking). The first algorithm EWLS is an iterated local search algorithm that works with a partial vertex cover, and utilizes an edge weighting scheme which updates edge weights when getting stuck in local optima. Nevertheless, EWLS has an instance-dependent parameter. Further, we propose a strategy called Configuration Checking for handling the cycling problem in local search. This is used in designing a more efficient algorithm that has no instance-dependent parameters, which is referred to as EWCC. Unlike previous vertex-based heuristics, the configuration checking strategy considers the induced subgraph configurations when selecting a vertex to add into the current candidate solution. A detailed experimental study is carried out using the well known DIMACS and BHOSLIB benchmarks. The experimental results conclude that EWLS and EWCC are largely competitive on DIMACS benchmarks, where they outperform other current best heuristic algorithms on most hard instances, and dominate on the hard random BHOSLIB benchmarks. Moreover, EWCC makes a significant improvement over EWLS, while both EWLS and EWCC set a new record on a twenty-year challenge instance. Further, EWCC performs quite well even on structured instances in comparison to the best exact algorithm we know. We also study the run-time behavior of EWLS and EWCC which shows interesting properties of both algorithms.

Agents learning to act autonomously in realworld domains must acquire a model of the dynamics of the domain in which they operate. Learning domain dynamics can be challenging, especially where an agent only has partial access to the world state, and/or noisy external sensors. Even in standard STRIPS domains, existing approaches cannot learn from noisy, incomplete observations typical of real-world domains. We propose a method which learns STRIPS action models in such domains, by decomposing the problem into first learning a transition function between states in the form of a set of classifiers, and then deriving explicit STRIPS rules from the classifiers' parameters. We evaluate our approach on simulated standard planning domains from the International Planning Competition, and show that it learns useful domain descriptions from noisy, incomplete observations.

The inference problem in propositional logic realizes a strong connection between Artificial Intelligence and Operational Research. It is now well-known that this problem can be formulated as a constraint satisfaction problem (CSP), whose system has a generalized covering type (we recall that a CSP consists in proving the emptiness of a domain defined by a set of diophantine constraints, or the existence of a solution). We propose a new methoddenoted by FAST (Fast Algorithm for the constraint Satisfaction Test problems)-which allows an efficient solution of the CSP instances for logical inference. Computational results are reported for 3-SAT, 4SAT and system expert type instances.

Heuristic search procedures that aspire to find global optimal solutions to hard combinatorial optimization problems usually require some type of diversification to overcome local optimality. One way to achieve diversification is to re-start the procedure from a new solution once a region has been explored. In this chapter we describe the best known multi-start methods for solving optimization problems. We propose classifying these methods in terms of their use of randomization, memory and degree of rebuild. We also present a computational comparison of these methods on solving the linear ordering problem in terms of solution quality and diversification power.

In this article we approach the linear ordering problem with cumulative costs (LOPCC). Bertacco developed this problem [2] and propose two exact algorithms, due to the complexity of the problem Duarte propose a Tabu algorithm for LOPCC [3] and until now that algorithm is the state of the art. In this ongoing research we propose a set of iterated local search algorithms (ILS) to solve the LOPCC. The experimental evidence shows that the performance of the iterated local search algorithms evaluated have similar quality to the best solution reported and get better efficiency than the reference solution. Also with the local search algorithms we improve the best known solution for 32 instances. Now we are working in developing new algorithms with population metaheuristics.

Proximity searching consists of retrieving from a database those elements that are similar to a query object. The usual model for proximity searching is a metric space where the distance, which models the proximity, is expensive to compute. An index uses precomputed distances to speedup query processing. Among all the known indices, the baseline for performance for about 20 years has been AESA. This index uses an iterative procedure, where at each iteration it first chooses the next promising element (“pivot”) to compare to the query, and then it discards database elements that can be proved not relevant to the query using the pivot. The next pivot in AESA is chosen as the one minimizing the sum of lower bounds to the distance to the query proved by previous pivots. In this article, we introduce the new index iAESA , which establishes a new performance baseline for metric space searching. The difference with AESA is the method to select the next pivot. In iAESA, each candidate sorts...

La commutation tout-optique d'étiquettes (All-Optical Label Switching, AOLS) est une nouvelle technologie permettant le traitement des paquets sans conversion optique-électronique-optique. Dans ce rapport nous étudions le problème de router un ensemble de requêtes dans un réseau AOLS avec l'objectif de minimiser le nombre d'étiquettes nécessaires au routage des paquets. Nous utilisons la technique de l'empilement d'étiquettes pour configurer des tunnels et ainsi réduire la taille de l'espace des étiquettes. Nous étudions plus particulièrement ce problème de design pour des réseaux ayant une topologie de chemin. Nous proposons un algorithme exacte dans le cas où toutes les requêtes sont issues de la même source. Nous présentons également des algorithmes approchés et heuristiques pour du trafic général. Nous évaluons les performances de nos algorithmes par simulations.

Several approaches have been developed for answering users' specific questions about AI behavior and for assessing their core functionality in terms of primitive executable actions. However, the problem of summarizing an AI agent's broad capabilities for a user is comparatively new. This paper presents an algorithm for discovering from scratch the suite of high-level "capabilities" that an AI system with arbitrary internal planning algorithms/policies can perform. It computes conditions describing the applicability and effects of these capabilities in user-interpretable terms. Starting from a set of user-interpretable state properties, an AI agent, and a simulator that the agent can interact with, our algorithm returns a set of high-level capabilities with their parameterized descriptions. Empirical evaluation on several game-based scenarios shows that this approach efficiently learns descriptions of various types of AI agents in deterministic, fully observable settings. User studies show that such descriptions are easier to understand and reason with than the agent's primitive actions.

Given a graph $G$, a $k$-sparse $j$-set is a set of $j$ vertices inducing a subgraph with maximum degree at most $k$. A $k$-dense $i$-set is a set of $i$ vertices that is $k$-sparse in the complement of $G$. As a generalization of Ramsey numbers, the $k$-defective Ramsey number $R_k^{\mathcal{G}}(i,j)$ for the graph class $\mathcal{G}$ is defined as the smallest natural number $n$ such that all graphs on $n$ vertices in the class $\mathcal{G}$ have either a $k$-dense $i$-set or a $k$-sparse $j$-set. In this paper, we examine $R_k^{\mathcal{G}}(i,j)$ where $\mathcal{G}$ represents various graph classes. In forests and cographs, we give formulas for all defective Ramsey numbers. In cacti, bipartite graphs and split graphs, we provide defective Ramsey numbers in most of the cases and point out open questions, formulated as conjectures if possible.

A greedy Graph Coloring Algorithm allocates non-identical colors to the adjacent vertices of a graph such that the number of assigned colors is minimized. In Greedy Coloring of the graph, the ordering of vertices is an essential parameter for allocating the colors to vertices of a graph. Assigning the color to the graph must be time efficient. In this paper, we have proposed a new algorithm in which the Depth First Search algorithm is used to give orders to the vertices of the graph. The objective of this work is to develop a fast algorithm of graph coloring to overcome the problems in existing methods, and it should be efficient for all kinds of graph instances. The proposed algorithm is computed on large and small benchmark graphs and compared with four well known coloring algorithms BC-COL Algorithm, DSATUR Algorithm, A cutting plane Algorithm and new DSATUR Algorithm. The computation result shows that the proposed algorithm has successfully evaluated the known chromatic number for 54 different graphs and perform best with all other compared algorithm. It also tells the minimum number of colors required to color 19 different graphs whose chromatic numbers are not known.

We study, in the context of the Unit-Demand Vehicle Routing Problem, the relationship between the linear programming relaxation of a single-commodity flow model and the linear programming relaxation of a pure time-dependent formulation that is closely related to a formulation of the travelling salesman problem. We show that the time-dependent formulation implies a new large class of upper bounding and lower bounding flow constraints that are not implied by the linear programming of the single commodity flow model. Using the timedependent formulation we also show how to generate two new sets of inequalities in the space of the design variables: one set contains inequalities that are related to the well-known multistar constraints while the other contains inequalities that are related to double jump inequalities. Computational results show that the time dependent formulation can be used to easily solve instances with up to 80 nodes, when the vehicle capacity is reasonably small.

With the remarkable growth of portable application and the increasing frequency and integration density, power is being given comparable weight to speed and area in IC designs. In technology mapping, how decomposition is done can have a significant impact on the power dissipation of the final implementation. In the literature, only heuristic algorithms are given for the low-power gate decomposition problem. In this paper, we prove many properties an optimal decomposition tree must have. Based on these optimality properties, we design an efficient exact algorithm to solve the low-power gate decomposition problem. Moreover, the exact algorithm can be easily modified to a heuristic algorithm which performs much better than the known heuristics.

Abstmct-Given a set of input points, the rectilinear Steiner tree problem is to find a minimal length tree consisting of vertical and horizontal line segments that connects the input points, where it is possible to add new points to minimize the length of the tree. The restricted Steiner tree problem in which all the input points lie on the boundary of a rectangle frequently Occurs in VLSI physical design. Since the fastest published algorithm is cubic in the size of the point set, VLSI designers have been forced to use heuristic approximations to the length of the Steiner tree for this problem. We present a simple, practical, linear-time exact algorithm to find the Steiner tree for points lying on the boundary of a rectangle, obviating the need for some heuristic algorithms in VLSI design. The analysis of the algorithm is based on the use of a novel tie-breaking rule that should prove useful for other Steiner tree problems. ' * James P. Cohoon (M'82) received the B.S. degree in mathematics from Ramapo College of New Jersey, Mahwah, NJ in 1975, the M.S. degree in computer science from Pennsylvania State University, State College, PA in 1978, and the Ph.D. degree in computer science from the University of Minnesota, Minneapolis, M N in 1982. In 1983, he became an Assistant Professor in the Department of Computer Science at the University of Virginia, Charlottesville, VA. He is currently an Associate Professor there. His pri-COHOON el U /. : OPTIMAL STEINER TREE ALGORITHM _", mary research interests are in various aspects of computer-aided design, with particular emphasis on circuit layout. Other research interests include computational geometry, parallel algorithms, and heuristic search. Dr. Cohoon is a member of the ACM, SIGACT, SIGDA, and Upsilon Pi Epsilon. He is a member of the SIGDA Board of Directors and has served on the programming committee for IEEE International Conference on Computer-Aided Design. * rithms, with an emphasis on combinatorial applications and parallel implementations. Particular problems include graph algorithms, information dissemination in networks, parallel sorting, biological sequence analysis, Steiner trees, and new paradigms for combinatorial optimization.

A new method is introduced for packing items in convex regions of the Euclidian ndimensional space. By means of this approach the packing problem becomes a global finitedimensional continuous optimization problem. The strategy is based on the new concept of sentinels. Sentinels sets are finite subsets of the items to be packed such that, when two items are superposed, at least one sentinel of one item is in the interior of the other. Minimal sets of sentinels are found in simple 2−dimensional cases. Numerical experiments and pictures showing the potentiality of the new technique are presented.

It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for non-preemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem. In generalized multiprocessor scheduling (GMS) we have a job-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS) the only feasible schedules are preemptive schedules with the smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions. For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. Our scheme for a fixed number of machines has linear running time, and can be applied also for instances where jobs have release dates, and for instances with arbitrary preemption costs. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule. Our results for MPS hold for any instance in which a job, J j , can be processed simultaneously by ρ j machines, for some ρ j ≥ 1.

In this paper we deal with the Minimum Span Frequency Assignment Problem (MSFAP), that is the problem of assigning a limited set of radio frequencies to the base stations of a radio network so as the bandwidth occupancy is minimized and the overall interference is not too large. We present a new integer linear formulation for MSFAP in the multidemand case, which is the basis of an exact algorithm to compute both lower and upper bounds for MSFAP. Frequency assignments are represented as walks (sequence of nodes) in a graph. We look for a walk of minimum span, where the span of a walk is defined as the cost of a maximum cost subwalk (subsequence). The new approach is able to find optimum solutions over a large set of classical benchmarks.

The balanced traveling salesman problem (BTSP) is a variant of the traveling salesman problem, in which one seeks a tour that minimizes the difference between the largest and smallest edge costs in the tour. The BTSP, which is obviously NP-hard, was first investigated by Larusic and Punnen in 2011 [9]. They proposed several heuristics based on the double-threshold framework, which converge to good-quality solutions though not always optimal (e.g. 27 provably optimal solutions were found among 65 TSPLIB instances of at most 500 vertices). In this paper, we design a special-purpose branch-and-cut algorithm for solving exactly the BTSP. In contrast with the classical TSP, due to the BTSP's objective function, the efficiency of algorithms for solving the BTSP depends heavily on determining correctly the largest and smallest edge costs in the tour. In the proposed branch-and-cut algorithm, we develop several mechanisms based on local cutting planes, edge elimination, and variable fixing to locate more and more precisely those edge costs. Other important ingredients of our algorithm are heuristics for improving the lower and upper bounds of the branch-and-bound tree. Experiments on the same TSPLIB instances show that our algorithm was able to solve to optimality 63 out of 65 instances.

In this paper we present a portable exact parallel algorithm for the maximum clique problem on general graphs. Computational results with random graphs and some test graphs from applications are presented. The algorithm is parallelized using the Message Passing Interface (MPI) standard. The algorithm is based on the Carraghan-Pardalos exact algorithm (for unweighted graphs) and incorporates a variant of the greedy randomized adaptive search procedure (GRASP) for maximum independent set of Feo, Resende, and Smith (1994) to obtain good starting solutions.

Our work is intended to model and solve artificial planning problems with logic based planning, using the novel semantics called p-stable, which is an alternative of stable semantics. Also we present a method to encode a general planning problem and then we present an example, which is the blocks world problem. This can be applied in a variety of tasks including robotics, process planning, updates, making evacuation plans and so on.

The use of ant colony optimization algorithms for solving the routing problem in a process of products delivery taking into account a city transport infrastructure has shown in this research. The vehicle routing problem belongs to NP-hard task and its solution requires significant computing resources. Therefore, it is recommended to use metaheuristic methods to solve such problems including ant colony optimization algorithms. Solution of the Vehicle Routing Problem will cause a decrease of enterprises non-productive resources consumption and will promote the increase of their efficiency and competitiveness. The test example, consisting of eight consumers of freight and two transportation means with unlimited load capacity, moving around the certain city, is used for the implementation of the model. It can be further refined by taking into account various parameters besides transport infrastructure, including limitations on carrying capacity, a number of vehicles an working hours, an...