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International Conference on Nonlinear Programming and Variational Inequalities

作者： Charnsethikul, P Kasetsart Univ Dept Ind Engn Operat Res Unit Bangkok Thailand Kasetsart Univ Dept Ind Engn Management Sci Unit Bangkok Thailand

The minimax linear assignment problem with additional linear constraints is studied. An exact polynomial time algorithm is developed, verified and validated in case of a single added constraint. In case of multiple constraints, the problem is more complex and becomes NP-hard. A tree search technique is proposed. Some computational studies are reported.

关键词： combinatorial optimization polynomial time algorithm branch and bound method

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Solving problems of discrete tomography: Application in workforce scheduling

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4OR 2005年第4期3卷 337-340页

作者： Jarray, Fethi Laboratoire CEDRIC CNAM 75003 Paris 292 rue Saint-Martin France

This is a summary of the most important results presented in the author's PhD thesis. This thesis, written in French, was defended on 24 November 2004 and supervised by Marie-Christine Costa and Christophe Picouleau. This thesis consists in developing the study of discrete tomography problems. It aims at reconstructing discrete objects (matrices, images, discrete sets, etc) that are accessible only through few projections. A copy of the thesis is available on "http: //***/***?id = 698". © Springer-Verlag 2005.

关键词： Discrete tomography Image reconstruction Maximum flow polynomial time algorithm Workforce scheduling

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On the Impact of Coding Parameters on Storage Requirement of Region-based Fault Tolerant Distributed File System Design

On the Impact of Coding Parameters on Storage Requirement of...

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International Conference on Computing, Networking and Communications (ICNC)

作者： Banerjee, Sujogya Das, Arun Mazumder, Anisha Derakhshandeh, Zahra Sen, Arunabha Arizona State Univ Sch Comp Informat & Decis Syst Engn Comp Sci & Engn Program Tempe AZ 85287 USA

ISBN: (纸本)9781479923588

Advances in technology have resulted in Internet-scale deployment of storage systems such as peer-to-peer storage and cloud storage, where data is distributed over multiple storage nodes in a networked environment. In these environments the storage nodes are often commodity machines and are susceptible to failure. The notion of fault domain, introduced by Microsoft Azure, captures the fault-tolerance aspects of a data center. A fault domain is defined as a set of servers all of which become inaccessible when a single fault (such as the failure of a switch or a router) occurs in the data center. As such a fault domain can be viewed as a spatially correlated or region based failure. In order to enhance reliability through redundancy, maximum distance separable (MDS) codes such as Reed-Solomon codes and (N, K) codings are utilized. In this paper we present analytical results demonstrating that the choice of the coding parameters N and K may have significant impact on storage that will be necessary to achieve reliability. We present a polynomial time algorithm for optimal storage allocation in a mesh network and we conduct extensive experimentation to evaluate the impact of the coding parameters Ar and K on the storage requirement to provide all region fault tolerance with varying size of the mesh and the fault region.

关键词： Internet computational complexity computer centres distributed databases encoding fault tolerant computing network operating systems storage management system recovery Internet-scale deployment MDS codes Microsoft Azure Reed-Solomon codes cloud storage coding parameters commodity machines data center fault-tolerance aspects maximum distance separable codes mesh network optimal storage allocation peer-to-peer storage polynomial time algorithm region based failure region-based fault tolerant distributed file system design spatially correlated failure storage requirement storage systems Color Encoding Fault tolerance Fault tolerant systems Image color analysis Peer-to-peer computing Silicon

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Parametric algorithms for Cyclic Scheduling Problems with Applications to Robotics

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7th Mexican International Conference on Artificial Intelligence (MICAI 2008)

作者： Kats, Vladimir Levner, Eugene Inst Ind Math Beer Sheva Israel Bar Ilan Univ Holon Inst Technol IL-52100 Ramat Gan Israel

ISBN: (纸本)9783540886358

The paper considers cyclic scheduling problems arising in planning of robotic flowlines and logistics. The problems are reduced to finding the minimum (or maximum) cost-to-time ratio in doubly weighted graphs. New combinatorial algorithms are developed extending the cyclic project scheduling algorithm by Romanovskii (1967) and the minimum-cost-to-time-ratio algorithm by Dantzig, Blattner and Rao (1967). Whereas Romanovskii's and Dantzig-Blattner-Rao's algorithms are restricted to solving problems with fixed numerical data, the new algorithms can treat input data that are varied at prescribed intervals. Several special cases are solved in strongly polynomial time.

关键词： Cyclic scheduling robotic scheduling polynomial time algorithm intersection of polygons

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On the Thinness of Trees 7th

On the Thinness of Trees

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7th International Symposium on Combinatorial Optimization (ISCO)

作者： Bonomo-Braberman, Flavia Brandwein, Eric Lucia Gonzalez, Carolina Sansone, Agustin Univ Buenos Aires Fac Ciencias Exactas & Natur Dept Computac Buenos Aires Argentina Univ Buenos Aires Inst Invest Ciencias Computac ICC CONICET Buenos Aires Argentina

ISBN: (纸本)9783031185298;9783031185304

The study of structural graph width parameters like tree-width, clique-width and rank-width has been ongoing during the last five decades, and their algorithmic use has also been increasing [Cygan et al., 2015]. New width parameters continue to be defined, for example, mim-width in 2012, twin-width in 2020, and mixed-thinness, a generalization of thinness, in 2022. The concept of thinness of a graph was introduced in 2007 by Mannino, Oriolo, Ricci and Chandran, and it can be seen as a generalization of interval graphs, which are exactly the graphs with thinness equal to one. This concept is interesting because if a representation of a graph as a k-thin graph is given for a constant value k, then several known NP-complete problems can be solved in polynomial time. Some examples are the maximum weighted independent set problem, solved in the seminal paper by Mannino et al., and the capacitated coloring with fixed number of colors [Bonomo, Mattia and Oriolo, 2011]. In this work we present a constructive O(n log(n))-time algorithm to compute the thinness for any given n-vertex tree, along with a corresponding thin representation. We use intermediate results of this construction to improve known bounds of the thinness of some special families of trees.

关键词： Trees Thinness polynomial time algorithm

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Inventory replenishment planning with a full truckload cost and a full return policy

Inventory replenishment planning with a full truckload cost ...

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16th IFAC Symposium on Information Control Problems in Manufacturing (INCOM)

作者： Farhat, Mlouka Akbalik, Ayse Sauer, Nathalie Hadj-Alouane, Atidel B. Univ Lorraine LGIPM Technopole F-57073 Metz France Univ Lorraine LCOMS Technopole F-57073 Metz France Univ Tunis El Manar OASIS Ecole Natl Ingenieurs Tunis BP 37 Le Belvedere Tunis 1002 Tunisia

This paper addresses the single-item uncapacitated lot sizing problem with batch ordering under the buyback contract between a retailer and a supplier. The form of this type of contract consists in returning all the unused products at the end of every w periods (with w >= 1) to the supplier. This problem is studied with only full batches (OFB), which means that the procurement in each period is restricted to a multiple of a constant batch size, where each demand is satisfied without backlogging and all cost parameters are time-dependent. In this extension, we consider a stepwise discontinuous procurement cost structure due to the fixed cost per batch replenished, incurred by the retailer, in addition to the classical lot sizing costs. Several properties of the optimal solution are proposed to develop an efficient dynamic programming algorithm performed in time complexity O(Tw). (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Lot sizing replenishment planning buyback contract stepwise cost polynomial time algorithm

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A Greedy algorithm for Reconstructing Binary Matrices with Adjacent 1s 18th

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18th International Workshop on Combinatorial Image Analysis (IWCIA)

作者： Jarray, Fethi Tlig, Ghassen Cedric CNAM 292 Rue St Martin Paris France Higher Inst Comp Sci Medenine Medenine Tunisia Higher Inst Comp Sci Tunis LIMTIC Tunis Tunisia

ISBN: (纸本)9783319591087;9783319591070

This paper deals with the reconstruction of special cases of binary matrices with adjacent 1s. Each element is horizontally adjacent to at least another element. The projections are the number of elements on each row and column. We give a greedy polynomial time algorithm to reconstruct such matrices when satisfying only the vertical projection. We show also that the reconstruction is NP-complete when fixing the number of sequence of length two and three per row and column.

关键词： Discrete objects polynomial time algorithm Binary matrices reconstruction NP-completeness

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An acyclic days-off scheduling problem

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4OR 2006年第1期4卷 73-85页

作者： Costa, Marie-Christine Jarray, Fethi Picouleau, Christophe Laboratoire CEDRIC 75003 Paris 292 rue Saint-Martin France

This paper studies the days off scheduling problem when the demand for staffing fluctuates from day to another and when the number of total workdays is fixed in advance for each employee. The scheduling problem is then to allocate rests to employees with different days off policies: (1) two or three consecutive days off for each employee per week and (2) at least three consecutive days off for each employee per month. For each one, we propose a polynomial time algorithm to construct a solution if it exists. © Springer-Verlag 2006.

关键词： Acyclic scheduling Discrete tomography Maximum flow polynomial time algorithm Workforce scheduling

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A new efficient algorithm for weighted vertex cover in bipartite graphs based on a dual problem 9

A new efficient algorithm for weighted vertex cover in bipar...

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9th International Conference on Information Technology in Medicine and Education (ITME)

作者： Zhang Yujiao Duan Xia Yue Xuerong Chen Zhibin Kunming Univ Sci & Technol Dept Math Fac Sci Kunming Yunnan Peoples R China

ISBN: (纸本)9781538677438

The (un-weighted) vertex cover problem in general graphs is a classical NP-hard problem, but it is polynomial time solvable in bipartite graphs. This paper considers two combinatorial optimization problems. One is the weighted vertex cover problem and the other is the so-called maximum edge packing problem. We proved that in bipartite graphs, maximum edge packing problem can be viewed as the dual of the weighted vertex cover problem, and hence these two problems are polynomial time solvable. We explored the relationships between these two problems in bipartite graphs and some structural results are obtained accordingly. Furthermore, a new efficient algorithm for the weighted vertex cover problem in bipartite graphs is also derived. Our method generalized some previous algorithms for un-weighted vertex cover in bipartite graphs.

关键词： matching vertex cover edge packing polynomial time algorithm dual problem

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Reconstruction of binary matrices under adjacency constraints

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Electronic Notes in Discrete Mathematics 2005年 20卷 281-297页

作者： Costa, M.-C. Jarray, F. Picouleau, C. CEDRIC CNAM 75003 Paris 292 rue Saint Martin France CEDRIC CNAM 75003 Paris 292 rue Saint Martin France

We consider a generalization of the classical binary matrix reconstruction problem by considering adjacency constraints between the cells: if a given cell is of value 1 then all its neighbors are of value 0. This problem arises especially on statistical physics. We consider several definitions of neighborhood and for each one we give complexity results, necessary and/or sufficient conditions for the existence of a solution and in some cases, polynomial time algorithms. © 2005 Elsevier B.V. All rights reserved.

关键词： adjacency constraint binary matrix reconstruction Discrete tomography network flow NP-complete polynomial time algorithm

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