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Comments on "Flow shop and open shop scheduling with a critical machine and two operations per job"

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第1期157卷 257-261页

作者： Mosheiov, G Yovel, U Hebrew Univ Jerusalem Sch Business Adm IL-91905 Jerusalem Israel Hebrew Univ Jerusalem Dept Stat IL-91905 Jerusalem Israel Hebrew Univ Jerusalem Dept Comp Sci IL-91904 Jerusalem Israel

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 polynomial time 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.

关键词： scheduling flow-shop minimum makespan polynomial time algorithm

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Energy Efficient Delivery of Immersive Video Centric Services

Energy Efficient Delivery of Immersive Video Centric Service...

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IEEE INFOCOM Conference

作者： Llorca, Jaime Guan, Kyle Atkinson, Gary Kilper, Daniel C. Alcatel Lucent Bell Labs Holmdel NJ 07733 USA

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 polynomial time.

关键词： immersive video service multi-view video (MVV) energy efficiency integral polyhedron totally uni-modular polynomial time algorithm

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Reconstructing a binary matrix under timetabling constraints

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Electronic Notes in Discrete Mathematics 2005年 20卷 99-112页

作者： Picouleau, C. Brunetti, S. Frosini, A. CEDRIC CNAM 75003 Paris 292 rue Saint Martin France Department of Mathematics Roberto Magari University of Siena 53100 Siena Pian dei Mantellini 44 Italy

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 M_{i j} = 1 then M_{i j - 1} = 1 or M_{i j + 1} = 1, and the maximal number of successive 0's on each row of M is not greater than k. We furnish a polynomial time algorithm for reconstructing M by reducing this problem to that of finding a path of given weight in a weighted directed acyclic graph. © 2005 Elsevier B.V. All rights reserved.

关键词： binary matrix directed acyclic graph discrete tomography dynamic programming polynomial time algorithm

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Routing and Scheduling Problems with Two Agents on a Line-Shaped Network 1

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15th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： Yan, Hao Lu, Xiwen East China Univ Sci & Technol Dept Math Shanghai 200237 Peoples R China

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) time algorithm 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.

关键词： Network scheduling Agent scheduling polynomial time algorithm Approximation algorithm

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The Complexity and algorithm for Minimum Expense Spanning Trees

The Complexity and Algorithm for Minimum Expense Spanning Tr...

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International Workshop on Information and Electronics Engineering (IWIEE) / International Conference on Information, Computing and Telecommunications (ICICT)

作者： Zhan Ning Wu Longshu China Jiliang Univ Coll Sci Hangzhou 310018 Peoples R China Xinyang Vocat & Tech Coll Math & Comp Sci Dept Xinyang 464000 Peoples R China

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.

关键词： Minimum expense spanning tree Computational complexity polynomial time algorithm Combinatorial optimization NP-hard

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The Volume of a Crosspolytope Truncated by a Halfspace 1

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15th Annual Conference on Theory and Applications of Models of Computation (TAMC)

作者： Ando, Ei Tsuchiya, Shoichi Senshu Univ Tama Ku 2-1-1 Higashi Mita Kawasaki Kanagawa 2148580 Japan

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)) time algorithm 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.

关键词： polynomial time algorithm Volume computation Geometric duality

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SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING timeS AND COMPRESSION COSTS （PART I：EQUAL timeS AND COSTS）

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Applied Mathematics(A Journal of Chinese Universities) 1998年第4期13卷 417-426页

作者： TANGGUOCHUN FOULDS,L.R. DepartmentofManagement ShanghaiSecondPolytechncUniversityShanghai200002. DepartmentofManagementSystems UniversityofWaikatoHamiltonNewZealand

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.

关键词： Machine scheduling problems controllable processing times uniform compression timeand cost dominance set lateness crash activities polynomial time algorithm

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Finding gale strings

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 1065-1072页

作者： Casetti, Marta M. Merschen, Julian von Stengel, Bernhard Dept. of Mathematics London School of Economics London WC2A 2AE United Kingdom

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 argument. For bimatrix games, this argument is provided by the Lemke-Howson algorithm. It has been shown that this algorithm is worst-case exponential with the help of dual cyclic polytopes, where the algorithm can be expressed combinatorially via labeled bitstrings defined by the "Gale evenness condition" that characterize the vertices of these polytopes. We define the combinatorial problem Another completely labeled Gale string whose solutions define the Nash equilibria of games defined by cyclic polytopes, including games where the Lemke-Howson algorithm takes exponential time. If this problem was PPAD-complete, this would imply that 2-. Nash is PPAD-complete, in a much simpler way than the currently known proofs, including the original proof by Chen and Deng [Chen, X., and X. Deng (2006). Settling the complexity of two-player Nash equilibrium. Proc. 47th FOCS, 261-272]. However, we show that Another completely labeled Gale string is solvable in polynomial time by a simple reduction to Perfect matching in graphs, making it unlikely to be PPAD-complete. Although this result is negative, we hope that it stimulates research into combinatorially defined problems that are PPAD-complete and imply this property for 2-. Nash. © 2010 Elsevier B.V.

关键词： Complexity Gale Evenness Strings Lemke-Howson Nash Equilibria Perfect Matching polynomial time algorithm

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Solving Some Instances of the 2-Color Problem

Solving Some Instances of the 2-Color Problem

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15th International Conference on Discrete Geometry for Computer Imagery

作者： Brocchi, S. Frosini, A. Rinaldi, S. Univ Florence Dipartimento Sistemi & Informat Florence Italy Univ Siena Dept Sci Math & Informat Siena Italy

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 polynomial time 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 time algorithm 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.

关键词： Discrete tomography polynomial time algorithm k-color problem

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Capacitated Partial Inverse Maximum Spanning Tree Under the Weighted l_∞-norm 15th

Capacitated Partial Inverse Maximum Spanning Tree Under the ...

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15th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： Li, Xianyue Yang, Ruowang Zhang, Heping Zhang, Zhao Lanzhou Univ Sch Math & Stat Lanzhou 730000 Gansu Peoples R China Zhejiang Normal Univ Coll Math Phys & Informat Engn Jinhua 321004 Zhejiang Peoples R China

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-time algorithm for calculating the optimal value and an optimal solution.

关键词： Partial inverse problem Spanning tree polynomial time algorithm

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