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Intelligent Low-Code Platform As a Rule Construction Environment: A Spatial Methodology for Constructing Semantic graphical algorithms

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SCIENTIFIC AND TECHNICAL INFORMATION PROCESSING 2024年第5期51卷 412-421页

作者： Rogozov, Yu. I. Southern Fed Univ Taganrog Rostov Oblast Russia

In the first part of the article, the need to transition from subject to spatial methodology is substantiated, and a convergent approach for the convergence of the properties of the intelligence of space into its rules is proposed. In this article, the convergent approach is used to converge the manifested properties of the intelligence of space (gravitation, mutual influence of the geometry of space and matter, emergence, etc.) in the rules of spatial methodology. The existing entities of the geometric forms of rules of elementary distinction and the rules of their self-development are considered. The initial entity of the geometric form of the rule of the artificial preparation of the emergence effect and the process of its materialization in the initial semantic entity of the graphical algorithm of the implementation of an elementary action are proposed. The process of self-development of the initial entity of the graphical algorithm of the elementary action into the semantic graphical algorithm for bridging the gap or solving problems is shown. In the process of implementing the algorithm, the meaning will be transferred to the target matter.

关键词： intelligence of space geometric interpretation sense-making contradiction differences consciousness mechanism meaning action implementation emergence convergence graphical algorithm

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A graphical realization of the dynamic programming method for solving NP-hard combinatorial problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009年第4期58卷 619-631页

作者： Lazarev, Alexander A. Werner, Frank Russian Acad Sci Inst Control Sci Moscow 117997 Russia Otto VonGuericke Univ Magdegurg Fak Math D-39016 Magdeburg Germany

In this paper, we consider a graphical realization of dynamic programming. The concept is discussed on the partition and knapsack problems. In contrast to dynamic programming, the new algorithm can also treat problems with non-integer data without necessary transformations of the corresponding problem. We compare the proposed method with existing algorithms for these problems on small-size instances of the partition problem with n <= 10 numbers. For almost all instances, the new algorithm considers on average substantially less "stages" than the dynamic programming algorithm. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.

关键词： Dynamic programming Exact algorithm graphical algorithm Partition problem Knapsack problem

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A new graphical approach for solving single-machine scheduling problems approximately

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2014年第13期52卷 3762-3777页

作者： Gafarov, Evgeny R. Dolgui, Alexandre Werner, Frank Ecole Natl Super Mines UMR CNRS 6158 LIMOS F-42023 St Etienne France Russian Acad Sci Inst Control Sci Moscow Russia Univ Magdeburg Fak Math D-39106 Magdeburg Germany

Often the problem of determining an optimal or approximate production schedule in a company can be reduced to the problem of solving a scheduling problem on a bottleneck machine. However, even the majority of the resulting single-machine scheduling problems are NP-hard from a computational point of view and, therefore, it is difficult to solve large instances of such problems exactly. In this paper, we consider five such single-machine problems, where a dynamic programming algorithm of pseudo-polynomial complexity exists. The running time of such an algorithm can often be improved by so-called graphical algorithms which do not need to consider all states in a dynamic programming algorithm separately. Based on such graphical algorithms, we present fully polynomial-time approximation schemes (FPTASes) for five single-machine total tardiness problems. The new FPTASes have the best running time among the known approximation schemes for these problems. The presented approach is rather general and can be applied to many other scheduling and combinatorial optimisation problems as well.

关键词： single-machine scheduling total weighted tardiness graphical algorithm fully polynomial-time approximation scheme

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A graphical approach to solve an investment optimization problem

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Journal of Mathematical Modelling and algorithms in Operations Research 2014年第4期13卷 597-614页

作者： Gafarov, Evgeny R. Dolgui, Alexandre Lazarev, Alexander A. Werner, Frank Ecole Nationale Superieure des Mines FAYOL-EMSE CNRS:UMR6158 LIMOS Saint-Etienne 42023 France Institute of Control Sciences of the Russian Academy of Sciences Profsoyuznaya st. 65 Moscow 117997 Russian Federation Higher School of Economics (National Research University) Moscow Russian Federation Lomonosov Moscow State University Moscow Russian Federation Moscow Institute of Physics and Technology (State University) Moscow Russian Federation Fakultät für Mathematik Otto-von-Guericke-Universität Magdeburg PSF 4120 Magdeburg 39016 Germany

We consider a project investment problem, where a set of projects and an overall budget are given. For each project, a piecewise linear profit function is known which describes the profit obtained if a specific amount is invested into this project. The objective is to determine the amount invested into each project such that the overall budget is not exceeded and the total profit is maximized. For this problem, a graphical algorithm (GrA) is presented which is based on the same Bellman equations as the best known dynamic programming algorithm (DPA) but the GrA has several advantages in comparison with the DPA. Based on this GrA, a fully-polynomial time approximation scheme is proposed having the best known running time. The idea of the GrA presented can also be used to solve somesimilar scheduling or lot-sizing problems in a more effective way, e.g., the related problem of finding lot-sizes and sequencing several products on a single imperfect machine. © Springer Science+Business Media Dordrecht 2014.

关键词： FPTAS graphical algorithm Project investment Pseudo-polynomial time complexity

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A note on a single machine scheduling problem with generalized total tardiness objective function

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INFORMATION PROCESSING LETTERS 2012年第3期112卷 72-76页

作者： Gafarov, Evgeny R. Lazarev, Alexander A. Werner, Frank Univ Magdeburg Fak Math D-39016 Magdeburg Germany Russian Acad Sci Inst Control Sci Moscow 117997 Russia Moscow MV Lomonosov State Univ Higher Sch Econ Moscow Inst Phys & Technol Moscow 117234 Russia

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Scheduling Single machine Total tardiness Number of tardy jobs Total late work Pseudo-polynomial algorithm graphical algorithm

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A graphical Approach to Solve Combinatorial Problems: algorithms and Some Computational Results

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IFAC Proceedings Volumes 2012年第6期45卷 127-132页

作者： Evgeny R. Gafarov Alexander A. Lazarev Frank Werner Institute of Control Sciences of the Russian Academy of Sciences Profsoyuznaya st. 65 117997 Moscow Russia Fakultät für Mathematik Otto-von-Guericke-Universität PSF 4120 39016 Magdeburg Germany

In this paper, we present a modification of dynamic programming algorithms ( DPA ), which we denote as graphical algorithms ( GrA ). For some single machine scheduling problems, it is shown that the time complexity of the GrA is less than the time complexity of the standard DPA. Moreover, the average running time of the GrA is often essentially smaller. A GrA can also solve large-scale instances and instances, where the parameters are not integer. For some problems, GrA has a polynomial time complexity in contrast to a pseudo-polynomial complexity of a DPA.

关键词： Dynamic programming Optimization Scheduling algorithms graphical algorithm Single machine algorithms

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A network theoretic method for the basic reproductive number for infectious diseases

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METHODS IN ECOLOGY AND EVOLUTION 2022年第11期13卷 2503-2515页

作者： Sisk, Anna Fefferman, Nina Univ Tennessee Dept Math Knoxville TN 37996 USA Univ Tennessee Dept Ecol & Evolutionary Biol Knoxville TN USA

When an outbreak of an infectious disease occurs, whether it is COVID-19 in humans, pine wilt in trees or canine distemper in dogs, quick and decisive actions need to be taken to contain it. One tool that can help both the scientific and applied management communities understand the infection risk during an outbreak is the basic reproductive number, Script capital R0$$ {\mathrm{\mathcal{R}}}_0 $$. In this paper, we use a network method to calculate and analyse the basic reproductive number, specifically flow network theory. We convert traditional compartmental models to flow networks and then apply the fundamental Max-Flow Min-Cut Theorem to calculate the basic reproductive number. We show that this method is equivalent to the traditional next generation matrix method for the calculation of Script capital R0$$ {\mathrm{\mathcal{R}}}_0 $$, and thus a valid alternative. Then we provide step-by-step instructions and illustrate how to apply this method to epidemic models. The current methods available for calculating Script capital R0$$ {\mathrm{\mathcal{R}}}_0 $$ are complicated, requiring mathematical training. This can act as a barrier to understanding and cause delays in a real-time response. Our new approach drastically reduces the mathematical complexity of the calculation and is far more accessible to the broader scientific community. It also allows for novel insights and can be applied to models/situations where traditional methods fail.

关键词： epidemic threshold epidemiological threshold graphical algorithm network calculation

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