Define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis. An algorithm is given that finds a cycle basis with the shortest possible length in O(m3n<span cla...
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Define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis. An algorithm is given that finds a cycle basis with the shortest possible length in O(m3n
Large amount of contents in the Internet have increased loads of contents servers, networks and data centers, which may degrade quality of service. To solve this problem, there is a method that some mirror servers pro...
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ISBN:
(纸本)9781467376952
Large amount of contents in the Internet have increased loads of contents servers, networks and data centers, which may degrade quality of service. To solve this problem, there is a method that some mirror servers providing the same contents are located on a network and a request is navigated to one of the mirror servers. As the location of the mirror servers affects the quality of service, it is important to locate the mirror servers in the network so that a network should connect a user and one of mirror servers with small hop length after links fail. In this paper, we address the server location problem that determines the location of the servers satisfying the following constraint: any users can access servers within a small hop count even if some links fail. In the previous research, we proved that this problem is NP-hard and proposed some heuristic algorithms. In this paper, we present a polynomial-time algorithm when the number of simultaneously failed links is restricted to one and the increase of hop length is restricted;in other words, we can get the optimum solution of the optimization version to minimize the number of servers in polynomialtime. Furthermore, we evaluate the performance of actual ISP network topologies by the algorithm from the viewpoint of the number of servers.
The sailing speed optimization problem aims to determine the optimal cruising speeds of ships by balancing the number of ships required on services, the fuel consumption, and the level of service provided for customer...
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The sailing speed optimization problem aims to determine the optimal cruising speeds of ships by balancing the number of ships required on services, the fuel consumption, and the level of service provided for customers. The level of service can be incorporated into a sailing speed optimization model from the perspective of supply chain management or from the perspective of shipping lines. We design a polynomial-time algorithm workable to solve the two models based on bi-section search methods. The novelties of the algorithm include constructing a new parameter on which the bi-section search will be executed and deriving a near-optimal solution by taking advantage of the problem structure. We also provide theoretical results that guarantee the validity of the polynomial-time algorithm. (C) 2016 Elsevier Ltd. All rights reserved.
This paper investigates computing completely positive (cp) decompositions of positive semi-definite (PSD) matrices, a problem which arises in many applications. We propose the first polynomial-time algorithm for check...
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This paper investigates computing completely positive (cp) decompositions of positive semi-definite (PSD) matrices, a problem which arises in many applications. We propose the first polynomial-time algorithm for checking if a given PSD matrix has cp-rank of at most r, when r is a given constant. In addition, we present a polynomial-time algorithm for computing a (rational) cp-decomposition of such a matrix if it exists, within any desired accuracy. (C) 2016 Elsevier B.V. All rights reserved.
We are given an n-node undirected ring network, in which each link of the ring is associated with a weight. Traffic demand is given for each pair of nodes in the ring. Each demand is allowed to be split into two integ...
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We are given an n-node undirected ring network, in which each link of the ring is associated with a weight. Traffic demand is given for each pair of nodes in the ring. Each demand is allowed to be split into two integer parts, which are then routed in different directions, clockwise and counterclockwise, respectively. The load of a link is the sum of the flows routed through the link and the nonnegative weighted load of a link is the product of its weight and its load. The objective is to find a routing scheme such that the maximum weighted load on the ring is minimized. Based on some useful structural properties of the decision version of the problem, we design a polynomial-time combinatorial algorithm for the optimization problem. (C) 2010 Elsevier B.V. All rights reserved.
In this paper, we give the first polynomialtimealgorithm to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Grobner basis of the Z[x]-module generated by the column...
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In this paper, we give the first polynomialtimealgorithm to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Grobner basis of the Z[x]-module generated by the column vectors of F. The algorithm has polynomial bit size computational complexities and is also shown to be practically more efficient than existing algorithms. The algorithm is based on three key ingredients. First, an F4 style algorithm to compute the Grobner basis is adopted, where a novel prolongation is designed such that the sizes of coefficient matrices under consideration are nicely controlled. Second, the complexity bound of the algorithm is achieved by a nice estimation for the degree and height bounds of the polynomials in the generalized Hermite normal form. Third, fast algorithms to compute Hermite normal forms of matrices over Z are used as the computational tool. (C) 2018 Elsevier B.V. All rights reserved.
A flow-shop batching problem with consistent batches is considered in which the processing times of all jobs on each machine are equal to p and all batch set-up times are equal to s. In such a problem, one has to part...
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A flow-shop batching problem with consistent batches is considered in which the processing times of all jobs on each machine are equal to p and all batch set-up times are equal to s. In such a problem, one has to partition the set of jobs into batches and to schedule the batches on each machine. The processing time of a batch B(i) is the sum of processing times of operations in B(i) and the earliest start of B(i) on a machine is the finishing time of B(i) on the previous machine plus the set-up time s. Cheng et al. (Naval Research Logistics 47:128-144, 2000) provided an O(n) pseudopolynomial-time algorithm for solving the special case of the problem with two machines. Mosheiov and Oron (European Journal of Operational Research 161: 285291, 2005) developed an algorithm of the same time complexity for the general case with more than two machines. Ng and Kovalyov (Journal of Scheduling 10: 353-364, 2007) improved the pseudopolynomial complexity to O(root n). In this paper, we provide a polynomial-time algorithm of time complexity O(log(3)n).
We present a simple polynomial-time algorithm that recognises reflexive, symmetric graphs admitting a near-unanimity operation. Several other characterisations of these graphs are also presented. (c) 2004 Elsevier Inc...
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We present a simple polynomial-time algorithm that recognises reflexive, symmetric graphs admitting a near-unanimity operation. Several other characterisations of these graphs are also presented. (c) 2004 Elsevier Inc. All rights reserved.
We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form ca...
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We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form can be converted into an unconstrained optimization problem. The relevant properties on the unconstrained optimization problem such as the duality, the boundedness of the solution and the path-following lemma, etc, are proved. Second, a self-concordant function on entire space which can be used as penalty for linear programming is constructed. For this specific function, more results are obtained. In particular, we show that, by taking a parameter large enough, the optimal solution for the unconstrained optimization problem is located in the increasing interval of the self-concordant function, which ensures the feasibility of solutions. Then by means of the self-concordant penalty function on entire space, a path-following algorithm on entire space for linear programming is presented. The number ofNewton steps of the algorithm is no more than O(nL log(nL/epsilon)), and moreover, in short step, it is no more than O(root n log(nL/epsilon)).
We consider a polynomial-time algorithm for the following scheduling problem: Given two machines, where each machine can process at most one job at a time;a set of jobs, where each job can start on or after its releas...
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We consider a polynomial-time algorithm for the following scheduling problem: Given two machines, where each machine can process at most one job at a time;a set of jobs, where each job can start on or after its release date and consists of a chain of unit-time operations such that the machines have to process them by turn begining with a given machine;find a schedule minimizing the maximum job completion time. Formerly, only pseudopolynomial-time algorithms have been proposed for this problem.
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