We propose an exact algorithm to determine the satisfiability of oblivious read-twice branching programs. Our algorithm runs in 2(1-Omega(1/log c))n time for instances with n variables and cn nodes.
We propose an exact algorithm to determine the satisfiability of oblivious read-twice branching programs. Our algorithm runs in 2(1-Omega(1/log c))n time for instances with n variables and cn nodes.
This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors' previous algorithm for the pro...
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This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors' previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of single-machine scheduling problems: the total weighted earliness-tardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.
We consider the problem [art gallery problem (AGP)] of minimizing the number of vertex guards required to monitor an art gallery whose boundary is an n-vertex simple polygon. In this paper, we compile and extend our r...
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We consider the problem [art gallery problem (AGP)] of minimizing the number of vertex guards required to monitor an art gallery whose boundary is an n-vertex simple polygon. In this paper, we compile and extend our research on exact approaches for solving the AGP. In prior works, we proposed and tested an exact algorithm for the case of orthogonal polygons. In that algorithm, a discretization that approximates the polygon is used to formulate an instance of the set cover problem, which is subsequently solved to optimality. Either the set of guards that characterizes this solution solves the original instance of the AGP, and the algorithm halts, or the discretization is refined and a new iteration begins. This procedure always converges to an optimal solution of the AGP and, moreover, the number of iterations executed highly depends on the way we discretize the polygon. Notwithstanding that the best known theoretical bound for convergence is Theta(n(3)) iterations, our experiments show that an optimal solution is always found within a small number of them, even for random polygons of many hundreds of vertices. Herein, we broaden the family of polygon classes to which the algorithm is applied by including non-orthogonal polygons. Furthermore, we propose new discretization strategies leading to additional trade-off analysis of preprocessing vs. processing times and achieving, in the case of the novel Convex Vertices strategy, the most efficient overall performance so far. We report on experiments with both simple and orthogonal polygons of up to 2500 vertices showing that, in all cases, no more than 15 minutes are needed to reach an exact solution, on a standard desktop computer. Ultimately, we more than doubled the size of the largest instances solved to optimality compared with our previous experiments, which were already five times larger than those previously reported in the literature.
Heuristics are widely applied to modularity maximization models for the identification of communities in complex networks. We present an approach to be applied as a post-processing to heuristic methods in order to imp...
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Heuristics are widely applied to modularity maximization models for the identification of communities in complex networks. We present an approach to be applied as a post-processing to heuristic methods in order to improve their performances. Starting from a given partition, we test with an exact algorithm for bipartitioning if it is worthwhile to split some communities or to merge two of them. A combination of merge and split actions is also performed. Computational experiments show that the proposed approach is effective in improving heuristic results. (C) 2012 Elsevier B.V. All rights reserved.
We present a new algorithm designed to solve floorplanning problems optimally. More precisely, the algorithm finds solutions to rectangle packing problems which globally minimize wirelength and avoid given sets of blo...
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We present a new algorithm designed to solve floorplanning problems optimally. More precisely, the algorithm finds solutions to rectangle packing problems which globally minimize wirelength and avoid given sets of blocked regions. We present the first optimal floorplans for 3 of the 5 intensely studied MCNC block packing instances and a significantly larger industrial instance with 27 rectangles and thousands of nets. Moreover, we show how to use the algorithm to place larger instances that cannot be solved optimally in reasonable runtime. (C) 2015 Elsevier B.V. All rights reserved.
The deployment problem of sensor nodes of Internet of things (IoT) can be abstracted as listing minimal dominating sets of a graph. The problem of listing all the minimal dominating sets in a graph can be converted to...
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The deployment problem of sensor nodes of Internet of things (IoT) can be abstracted as listing minimal dominating sets of a graph. The problem of listing all the minimal dominating sets in a graph can be converted to the problem of state space search among candidate vertex sets. The search and optimization technologies, such as the bidirectional search and branch cut, can be applied to solve the problem effectively. Our experiments show that the new algorithm can reduce the running time by at least an order of magnitude, compared to a state-of-the-art algorithm for listing all the minimal dominating sets.
Given a set R of m disjoint finite regions in the 2-dimensional plane, all regions having polygonal boundaries, and given a set D of n discs with fixed centers and radii, we consider the problem of finding a minimum c...
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Given a set R of m disjoint finite regions in the 2-dimensional plane, all regions having polygonal boundaries, and given a set D of n discs with fixed centers and radii, we consider the problem of finding a minimum cardinality subset D * subset of D such that every point in R is covered by at least one disc in D*. We show that this problem can be solved by using an iterative procedure that alternates between the solution of a traditional set-cover problem and the construction of the Laguerre-Voronoi diagram of a circle set. Computer experiments demonstrate the effectiveness of the proposed algorithm, particularly when the number vertical bar D*vertical bar of discs necessary to cover R is low. (C) 2021 Elsevier B.V. All rights reserved.
The Grouping Efficacy Index (GEI) is well-recognized as a measure of the quality of a solution to a part-machine clustering problem. During the past two decades, numerous approximation procedures (heuristics and metah...
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The Grouping Efficacy Index (GEI) is well-recognized as a measure of the quality of a solution to a part-machine clustering problem. During the past two decades, numerous approximation procedures (heuristics and metaheuristics) have been proposed for maximization of the GEI. Although the development of effective approximation procedures is essential for large part-machine incidence matrices, the design of computationally feasible exact algorithms for modestly sized matrices also affords an important contribution. This article presents an exact (branch-and-bound) algorithm for maximization of the GEI. Among the important features of the algorithm are (i) the use of a relocation heuristic to establish a good lower bound for the GEI;(ii) a careful reordering of the parts and machines;and (iii) the establishment of upper bounds using the minimum possible contributions to the number of exceptional elements and voids for yet unassigned parts and machines. The scalability of the algorithm is limited by the number of parts and machines, as well as the inherent structure of the part-machine incidence matrix. Nevertheless, the proposed method produced globally optimal solutions for 104 test problems spanning 31 matrices from the literature, many of which are of nontrivial size. The new algorithm also compares favorably to a mixed-integer linear programming approach to the problem using CPLEX.
We present a new exact algorithm to solve a challenging vehicle routing problem with split pickups and deliveries, named as the single-commodity split-pickup and split -delivery vehicle routing problem (SPDVRP). In th...
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We present a new exact algorithm to solve a challenging vehicle routing problem with split pickups and deliveries, named as the single-commodity split-pickup and split -delivery vehicle routing problem (SPDVRP). In the SPDVRP, any amount of a product col-lected from a pickup customer can be supplied to any delivery customer, and the demand of each customer can be collected or delivered multiple times by the same or different vehicles. The vehicle fleet is homogeneous with limited capacity and maximum route duration. This problem arises regularly in inventory and routing rebalancing applications, such as in bike -sharing systems, where bikes must be rebalanced over time such that the appropriate num-ber of bikes and open docks are available to users. The solution of the SPDVRP requires determining the number of visits to each customer, the relevant portions of the demands to be collected from or delivered to the customers, and the routing of the vehicles. These three decisions are intertwined, contributing to the hardness of the problem. Our new exact algo-rithm for the SPDVRP is a branch-price-and-cut algorithm based on a pattern-based mathe-matical formulation. The SPDVRP relies on a novel label-setting algorithm used to solve the pricing problem associated with the pattern-based formulation, where the label components embed reduced cost functions, unlike those classical components that embed delivered or collected quantities, thus significantly reducing the dimension of the corresponding state space. Extensive computational results on different classes of benchmark instances illustrate that the newly proposed exact algorithm solves several open SPDVRP instances and signifi-cantly improves the running times of state-of-the-art algorithms.
The multidimensional knapsack problem (MKP) is a well-known, strongly NP-hard problem and one of the most challenging problems in the class of the knapsack problems. In the last few years, it has been a favorite playg...
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The multidimensional knapsack problem (MKP) is a well-known, strongly NP-hard problem and one of the most challenging problems in the class of the knapsack problems. In the last few years, it has been a favorite playground for metaheuristics, but very few contributions have appeared on exact methods. In this paper we introduce an exact approach based on the optimal solution of subproblems limited to a subset of variables. Each subproblem is faced through a recursive variable-fixing process that continues until the number of variables decreases below a given threshold (restricted core problem). The solution space of the restricted core problem is split into subspaces, each containing solutions of a given cardinality. Each subspace is then explored with a branch-and-bound algorithm. Pruning conditions are introduced to improve the efficiency of the branch-and-bound routine. In all the tested instances, the proposed method was shown to be, on average, more efficient than the recent branch-and-bound method proposed by Vimont et al. [Vimont, Y., S. Boussier, M. Vasquez. 2008. Reduced costs propagation in an efficient implicit enumeration for the 0-1 multidimensional knapsack problem. J. Combin. Optim. 15(2) 165-178] and CPLEX 10. We were able to improve the best-known solutions for some of the largest and most difficult instances of the OR-LIBRARY data set [Chu, P. C., J. E. Beasley. 1998. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics 4(1) 63-86].
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