Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion an...
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Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules leads to progressive fragmentation of the available space, making defragmentation an important issue. We address this problem by proposing an online and an offline component for the defragmentation of the available space. We consider defragmenting the module layout on a reconfigurable device. This corresponds to solving a 2-D strip packing problem. Problems of this type are NP-hard in e strong sense, and previous algorithmic results are rather limited. Based on a graph-theoretic characterization of feasible packings, we develop a method that can solve 2-D defragmentation instances of practical size to optimality. Our approach is validated for a set of benchmark instances. We also discuss a simple strategy for dealing with online scenarios, called "least-interference fit" (LIF);we give a number of analytic results that allow a comparison of LIF with the best offline solution, and demonstrate that it works well on benchmark instances of moderate size.
The (unweighted) Maximum Satisfiability problem (MAxSAT) is: Given a Boolean formula in conjunctive normal form, find a truth assignment that satisfies the largest number of clauses. This paper describes exact algorit...
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The (unweighted) Maximum Satisfiability problem (MAxSAT) is: Given a Boolean formula in conjunctive normal form, find a truth assignment that satisfies the largest number of clauses. This paper describes exact algorithms that provide new upper bounds for MAXSAT. We prove that MAxSAT can be solved in time O(\F\ . 1.3803(K)), where \F\ is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time bounds O(\F\ . 1.3995(k)), where k is the maximum number of satisfiable clauses, and O(1.1279(\F\)), for the same problem. For MAX2SAT this implies a bound of O(1.2722(K)). (C) 2000 Academic Press.
The shortest path problem is one of the classic network problems. The objective of this problem is to identify the least cost path through a network from a pre-determined starting node to a pre-determined terminus nod...
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The shortest path problem is one of the classic network problems. The objective of this problem is to identify the least cost path through a network from a pre-determined starting node to a pre-determined terminus node. It has many practical applications and can be solved optimally via efficient algorithms. Numerous modifications of the problem exist. In general, these are more difficult to solve. One of these modified versions includes an additional constraint that establishes an upper limit on the sum of some other arc cost (e.g., travel time) for the path. In this paper, a new optimal algorithm for this constrained shortest path problem is introduced. Extensive computational tests are presented which compare the algorithm to the two most commonly used algorithms to solve it. The results indicate that the new algorithm can solve optimally very large problem instances and is generally superior to the previous ones in terms of solution time and computer memory requirements. This is particularly true for the problem instances that are most difficult to solve. That is, those on large networks and/or where the additional constraint is most constraining. (c) 2007 Elsevier Ltd. All rights reserved.
We study an NP-complete (and MaxSNP-hard) communication problem on tree networks, the so-called MULTICUT IN TREES: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at mo...
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We study an NP-complete (and MaxSNP-hard) communication problem on tree networks, the so-called MULTICUT IN TREES: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at most k tree edges whose removal separates all given pairs of nodes. MULTICUT has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomial time approximation algorithms. By way of contrast, we provide a simple fixed-parameter algorithm for MULTICUT IN TREES showing fixed-parameter tractability with respect to parameter k. Moreover, based on some polynomial time data reduction rules, which appear to be of particular interest from an applied point of view, we show a problem kernel for MULTICUT IN TREES by an intricate mathematical analysis. (c) 2005 Wiley Periodicals, Inc.
VERTEX COVERING BY PATHS ON TREES with applications in machine translation is the task to cover all vertices of a tree T = (V, E) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard ...
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VERTEX COVERING BY PATHS ON TREES with applications in machine translation is the task to cover all vertices of a tree T = (V, E) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard and has recently been solved by an exact algorithm running in O(4(C) center dot vertical bar V vertical bar(2)) time, where C denotes the maximum number of paths covering a tree vertex. We improve this running time to O(2(C) center dot C center dot vertical bar V vertical bar). On the route to this, we introduce the problem TREE-LIKE WEIGHTED HITTING SET which might be of independent interest. In addition, for the unweighted case Of VERTEX COVERING BY PATHS ON TREES, we present an exact algorithm using a search tree of size O(2(k) center dot k!), where k denotes the number of chosen covering paths. Finally, we briefly discuss the existence of a size-O(k(2)) problem kernel. (C) 2007 Elsevier B.V. All rights reserved.
We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P) This characterization finds applications in new polynomial-time ...
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We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P) This characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the NP-hard problem to delete a minimum number of rows or columns from a 0/1-matrix such that the remaining submatrix has the C I P (C) 2009 Elsevier Inc. All rights reserved
Given a set of polygonal curves, we present algorithms for computing a middle curve that serves as a representative for the entire set of curves. We require that the middle curve consists of vertices of the input curv...
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Given a set of polygonal curves, we present algorithms for computing a middle curve that serves as a representative for the entire set of curves. We require that the middle curve consists of vertices of the input curves and that it minimizes the maximum discrete Frechet distance to all input curves. We consider three different variants of a middle curve depending on in which order vertices of the input curves may occur on the middle curve, and provide algorithms for computing each variant. (C) 2020 Elsevier B.V. All rights reserved.
In this study, we develop a branch and bound solution algorithm to solve the workload smoothing problem. Our algorithm incorporates new formulas for dynamically computing a lower bound on the optimal value of the obje...
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In this study, we develop a branch and bound solution algorithm to solve the workload smoothing problem. Our algorithm incorporates new formulas for dynamically computing a lower bound on the optimal value of the objective function and for determining the earliest workstations for tasks. It also uses a fast heuristic for computing a good initial upper bound. A comprehensive experimental analysis is conducted in this study. The analysis demonstrates the outstanding performance of the algorithm and its efficiency in solving medium-sized workload smoothing problems.
This paper introduces the vehicle routing problem with partial outsourcing (VRPPO) in which a customer can be served by a single private vehicle, by a common carrier, or by both a single private vehicle and a common c...
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This paper introduces the vehicle routing problem with partial outsourcing (VRPPO) in which a customer can be served by a single private vehicle, by a common carrier, or by both a single private vehicle and a common carrier. As such, it is a variant of the vehicle routing problem with private fleet and common carrier (VRPPC). The objective of the VRPPO is to minimize fixed and variable costs of the private fleet plus the outsourcing cost. We propose two different path-based formulations for the VRPPO and solve these with a branch-and-price-and-cut solution method. For each path-based formulation, two different pricing procedures are designed and used when solving the linear relaxations by column generation. To assess the quality of the solution methods and gain insight in potential cost improvements compared with the VRPPC, we perform tests on two instance sets with up to 100 customers from the literature.
We present a new method of solving graph problems related to VERTEX COVER by enumerating and expanding appropriate sets of nodes. As an application, we obtain dramatically improved runtime bounds for two variants of t...
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We present a new method of solving graph problems related to VERTEX COVER by enumerating and expanding appropriate sets of nodes. As an application, we obtain dramatically improved runtime bounds for two variants of the VERTEX COVER problem. In the case of CONNECTED VERTEX COVER, we take the upper bound from O*(6k) to O*(2.7606(k)) without large hidden factors. For TREE COVER, we show a complexity of O*(3.2361(k)), improving over the previous bound of O*((2k)(k)). In the process, faster algorithms for solving subclasses of the Steiner tree problem on graphs are investigated.
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