A recent paper [Eur. J. Operat. Res. 127 (2000) 120] addresses a flow-shop scheduling problem, where (i) each of the it jobs is limited to at most two operations, and (ii) one of these operations is common for all the...
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A recent paper [Eur. J. Operat. Res. 127 (2000) 120] addresses a flow-shop scheduling problem, where (i) each of the it jobs is limited to at most two operations, and (ii) one of these operations is common for all the jobs. The paper introduces a polynomialtime solution algorithm for the problem, which appears to be surprisingly simple. Our short note contains several comments related to the correctness of the algorithm, to its complexity, to the proof of optimality and to a possible extension. (C) 2003 Elsevier B.V. All rights reserved.
We examine the basic energy tradeoffs between video transport and video processing for services such as multi-view video (MVV) streaming, where multiple media streams are combined and processed to create an immersive ...
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ISBN:
(纸本)9781467307758
We examine the basic energy tradeoffs between video transport and video processing for services such as multi-view video (MVV) streaming, where multiple media streams are combined and processed to create an immersive and personalized user experience. We analyze and compare the energy efficiency of different architectural options for the location of video processing functions and illustrate how the architecture of choice is influenced by the network topology, the users' view preferences, and the relative transport-processing energy efficiency. We provide an integer linear programming formulation for the energy efficient functional resource allocation problem, which we show it can be solved as a linear program, and an easily implementable algorithm that generates optimal solutions in polynomialtime.
Our focus is on the problem of reconstructing a m × n binary matrix M from its vertical and horizontal projections when the following additional constraints have to be satisfied: given an integer k ≥ 2, if Mi j ...
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We consider routing and scheduling problems with two agents on a line-shaped network in this paper. There are two agents and each agent has some jobs which are located in the network. Let L = (V, E) be a line-shaped n...
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ISBN:
(数字)9783030926816
ISBN:
(纸本)9783030926816;9783030926809
We consider routing and scheduling problems with two agents on a line-shaped network in this paper. There are two agents and each agent has some jobs which are located in the network. Let L = (V, E) be a line-shaped network, where V = {v(0)} boolean OR V-A boolean OR V-B is the set of n + 1 vertices and E is a set of edges. A job v is located at some vertex v, which is also denoted as v. The travel time d(u, v) is associated with each edge {u, v} is an element of E. The vehicle starts from an initial vertex v(0) is an element of V and visits all jobs for their processing. The objective is to find a route of the vehicle that minimizes the completion time of agent A under the constraint condition that the completion time of agent B is no more than the threshold value Q. We express this problem as line - 1 vertical bar C-max(B) <= Q vertical bar C-max(A). For the problem without release time, an O(n) timealgorithm is provided. For the problem with release time, we show that this problem is NP-hard even though there is only one job in agent B and the jobs in agent A have no release time. Finally we give a (3, 3)-approximation algorithm for the before general problem.
The minimum spanning tree problem is a classical and well-known combinatorial optimization problem. There exist many efficient algorithms such as the Kruskal algorithm and Prim algorithm to solve it. But in a real net...
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ISBN:
(纸本)9781627485852
The minimum spanning tree problem is a classical and well-known combinatorial optimization problem. There exist many efficient algorithms such as the Kruskal algorithm and Prim algorithm to solve it. But in a real network, the vertices as well as the edges may have weights, and there are many cases of the vertex weights according to the degrees of the vertices. In this paper, we consider the computational complexity of the minimum expense spanning tree problem, which is to find a spanning tree in a network with minimum total expenses. We show that this problem is NP-hard in some general situations. And we propose a polynomial time algorithm when computing all the weights of the vertices in a spanning tree. (C) 2012 Published by Elsevier Ltd.
In this paper, we consider the computation of the volume of an n-dimensional crosspolytope truncated by a halfspace. Since a crosspolytope has exponentially many facets, we cannot efficiently compute the volume by div...
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ISBN:
(数字)9783030148126
ISBN:
(纸本)9783030148119;9783030148126
In this paper, we consider the computation of the volume of an n-dimensional crosspolytope truncated by a halfspace. Since a crosspolytope has exponentially many facets, we cannot efficiently compute the volume by dividing the truncated crosspolytope into simplices. We show an O(n(6)) timealgorithm for the computation of the volume. This makes a contrast to the 0-1 knapsack polytope, whose volume is #P-hard to compute. The paper is interested in the computation of the volume of the truncated crosspolytope because we conjecture the following question may have an affirmative answer: Does the existence of a polynomial time algorithm for the computation of the volume of a polytope K imply the same for K's geometric dual? We give one example where the answer is yes.
Abstract Most papers in scheduling research have treated individual job processing times as fixed parameters. However, in many practical situations, a manager may control processing time by reallocating resources. In ...
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Abstract Most papers in scheduling research have treated individual job processing times as fixed parameters. However, in many practical situations, a manager may control processing time by reallocating resources. In this paper, authors consider a machine scheduling problem with controllable processing times. In the first part of this paper, a special case where the processing times and compression costs are uniform among jobs is discussed. Theoretical results are derived that aid in developing an O(n 2) algorithm to slove the problem optimally. In the second part of this paper, authors generalize the discussion to general case. An effective heuristic to the general problem will be presented.
The problem 2-. Nash of finding a Nash equilibrium of a bimatrix game belongs to the complexity class PPAD. This class comprises computational problems that are known to have a solution by means of a path-following ar...
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In the held of Discrete Tomography, the 2-color problem consists in determining a matrix whose elements are of two different types, starting from its horizontal and vertical projections. It is known that the one color...
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ISBN:
(纸本)9783642043963
In the held of Discrete Tomography, the 2-color problem consists in determining a matrix whose elements are of two different types, starting from its horizontal and vertical projections. It is known that the one color problem has a polynomialtime reconstruction algorithm, while, with k >= 2, the k-color problem is NP-complete. Thus, the 2-color problem constitutes an interesting example of a problem just in the frontier between hard and easy problems. In this paper we define a linear timealgorithm to solve a set of its instances, where some values of the horizontal and vertical projections are constant, while the others are upper bounded by a positive number proportional to the dimension of the problem. Our algorithm relies on classical studies for the solution of the one color problem.
Given an edge weighted graph, and an acyclic edge set, the goal of the partial inverse maximum spanning tree problem is to modify the weight function as small as possible such that there exists a maximum spanning tree...
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ISBN:
(纸本)9783030926816;9783030926809
Given an edge weighted graph, and an acyclic edge set, the goal of the partial inverse maximum spanning tree problem is to modify the weight function as small as possible such that there exists a maximum spanning tree with respect to the new weight function containing the given edge set. In this paper, we consider this problem with capacitated constraint under the weighted l(infinity)-norm. By studying the properties of the optimal value and a special kind of optimal solutions, combining the algorithm for the decision version of this problem with the Binary search method, we present a strongly polynomial-timealgorithm for calculating the optimal value and an optimal solution.
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