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53rd Southeastern International Conference on Combinatorics, Graph Theory, and Computing, SEICCGTC 2022

作者： Meyerowitz, Aaron Florida Atlantic University Boca RatonFL United States

We consider tilings of intervals and other sets in with translates of a three element integer set A={0,a,a+b} and its reflection b={0,b,a+b}. We also consider these questions for intervals and other sets in where a an... 详细信息

ISBN: (纸本)9783031621659

关键词： integer linear programming

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MatBuilder: Mastering Sampling Uniformity Over Projections

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ACM TRANSACTIONS ON GRAPHICS 2022年第4期41卷 p1-13页

作者： Paulin, Lois Bonneel, Nicolas Coeurjolly, David Iehl, Jean-Claude Keller, Alexander Ostromoukhov, Victor Univ Lyon LIRIS INSA Lyon UCBLCNRS Lyon France NVIDIA Munich Bavaria Germany

Many applications ranging from quasi-Monte Carlo integration over optimal control to neural networks benefit from high-dimensional, highly uniform samples. In the case of computer graphics, and more particularly in rendering, despite the need for uniformity, several sub-problems expose a low-dimensional structure. In this context, mastering sampling uniformity over projections while preserving high-dimensional uniformity has been intrinsically challenging. This difficulty may explain the relatively small number of mathematical constructions for such samplers. We propose a novel approach by showing that uniformity constraints can be expressed as an integer linear program that results in a sampler with the desired properties. As it turns out, complex constraints are easy to describe by means of stratification and sequence properties of digital nets. Formalized using generator matrix determinants, our new MatBuilder software solves the set of constraints by iterating the linear integer program solver in a greedy fashion to compute a problem-specific set of generator matrices that can be used as a drop-in replacement in the popular digital net samplers. The samplers created by MatBuilder achieve the uniformity of classic low discrepancy sequences. More importantly, we demonstrate the benefit of the unprecedented versatility of our constraint approach with respect to low-dimensional problem structure for several applications.

关键词： Path tracing quasi-Monte Carlo integration low discrepancy sequences generator matrices integer linear programming

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SCMA Codebooks Design for Three Optimization Algorithms Based on Eisenstein integer Unit Circle

SCMA Codebooks Design for Three Optimization Algorithms Base...

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2024 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2024

作者： Wan, Teng Ge, Wenping Ubul, Kurban Liao, Yifan College of Computer Science and Technology Xinjiang University Urumqi830046 China

ISBN: (纸本)9781665410205

Codebook design plays a crucial role in non-orthogonal sparse code multiple access technology. In this paper, a mother constellation constructed by the Eisenstein integer unit circle in the complex plane is proposed, and the power imbalance and dimensionality reduction are introduced into the codebook design. Three optimization algorithms are used to maximize the minimum Euclidean distance (MED) of superimposed codewords on the resource element as the objective function, and the optimal solution of the rotation angle is finally obtained, so as to obtain the three expected codebooks. Simulation results demonstrate that the proposed codebooks have smaller bit error rate (BER) and better performance than the four benchmark codebooks provided under the condition of a Gaussian channel. © 2024 IEEE.

关键词： integer linear programming

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Learning Optimal Signal Temporal Logic Decision Trees for Classification: A Max-Flow MILP Formulation 63

Learning Optimal Signal Temporal Logic Decision Trees for Cl...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Liang, Kaier Cardona, Gustavo A. Kamale, Disha Vasile, Cristian-Ioan Lehigh University Mechanical Engineering and Mechanics Department PA United States

ISBN: (纸本)9798350316339

This paper presents a novel framework for inferring timed temporal logic properties from data. The dataset comprises pairs of finite-time system traces and corresponding labels, denoting whether the traces demonstrate specific desired behaviors, e.g. whether the ship follows a safe route or not. Our proposed approach leverages decision-tree-based methods to infer Signal Temporal Logic classifiers using primitive formulae. We formulate the inference process as a mixed integer linear programming optimization problem, recursively generating constraints to determine both data classification, i.e., decision criteria and the tree structure. Applying a max-flow algorithm on the resultant tree transforms the problem into a global optimization challenge, leading to improved classification rates compared to prior methodologies. Moreover, we introduce a technique to reduce the number of constraints by exploiting the symmetry inherent in STL primitives, which enhances the algorithm's time performance and interpretability. We conduct three case studies involving two-class, multi-class, and complex formula classification scenarios to assess our algorithm's effectiveness and classification performance. © 2024 IEEE.

关键词： integer linear programming

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Image Encryption via QSD Decomposition and Pairing Functions: A Novel Approach 1

Image Encryption via QSD Decomposition and Pairing Functions...

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1st International Conference on Innovative and Intelligent Information Technologies, IC3IT 2024

作者： Harkati, Oussama Noui, Lemnouar Beloucif, Assia University of Batna 2 Lamie Laboratory Department of Computer Science Batna Algeria University of Batna 2 Lamie Laboratory Department of Mathematics Batna Algeria Institute of Hygiene and Industrial Safety University of Batna 2 Lamie Laboratory Batna Algeria

ISBN: (纸本)9798331541064

In today's digital world, information security is more important than ever. Cryptography, the science of encrypting data, plays a vital role in protecting sensitive information. However, with the development of attack threats and computational power the implementation of new cryptographic techniques and strategies becomes crucial to protect information. In this context, this paper presents a novel approach to encrypt grayscale images based on integer decomposition, called quasi-square decomposition, Cantor's pairing function and involutory matrix. Experimental results and security analysis demonstrate the effectiveness of the proposed approach, providing a robust solution for data protection. © 2024 IEEE.

关键词： integer linear programming

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Improving heuristics miners for healthcare applications by discovering optimal dependency graphs

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JOURNAL OF SUPERCOMPUTING 2022年第18期78卷 19628-19661页

作者： Tavakoli-Zaniani, Maryam Gholamian, Mohammad Reza Hashemi-Golpayegani, Seyyed Alireza Iran Univ Sci & Technol Sch Ind Engn Tehran Iran Amirkabir Univ Technol Comp Engn & Informat Technol Dept Tehran Iran

Dependency graph discovery is a substantial step in heuristic mining algorithms which are among the most prevalent process discovery methods in the healthcare domain due to their ability to deal with noisy event logs derived from unstructured and highly variable healthcare processes. However, in many healthcare applications, the current dependency graph discovery methods are still likely to create complex (spaghetti-like) and low-quality results. Hence, this paper improves the heuristic mining methods for healthcare applications by introducing a novel integer linear programming model for selecting the optimum set of dependency graph activities and arcs. The proposed method can lead to the extraction of dependency graphs that are simultaneously high-quality and non-complex. According to the assessments, when dealing with artificial and real-life healthcare event logs, the proposed method results in outputs with significantly less complexity and higher quality than the most prominent heuristic mining methods.

关键词： Process mining Process discovery Heuristic mining algorithms dependency graph discovery integer linear programming Healthcare processes

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Design of Optimal Control Sequences in Petri Nets Using Basis Marking Analysis

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第7期67卷 3685-3692页

作者： Ma, Ziyue Zou, Minqiang Zhang, Jiafeng Li, Zhiwu Xidian Univ Sch Electromech Engn Xian 710071 Peoples R China Macau Univ Sci & Technol Inst Syst Engn Taipa 999078 Macao Peoples R China

In this article, we develop an algorithm for designing an optimal control sequence in Petri nets, which drives a plant net from a source marking to a set of target markings without passing any pregiven forbidden markings. Such control sequences are useful in flexible reconfigurable automated systems, where a plant necessarily responds promptly to a request of reconfiguration. We develop a Dijkstra searching algorithm that is carried out in the basis marking space of a plant net instead of the conventional reachability space. Hence, only a small subset of the reachability set is explored, while the unpromising branches are reduced. Moreover, we propose a transition selecting rule to expose all forbidden trajectories and all first-met target markings during the searching process. The main advantage of the proposed method is wide applicability and low computational effort.

关键词： Petri nets Optimal control Aerospace electronics Trajectory integer linear programming Production Transportation Basis reachability graph (BRG) control sequence discrete-event system Petri net

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Quantifying the impact of sharing resources in a collaborative warehouse

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第2期302卷 518-529页

作者： Jamili, Negin van den Berg, Pieter L. de Koster, Rene Erasmus Univ Rotterdam Sch Management NL-3062 PA Rotterdam Netherlands

Collaboration in warehousing has the potential to decrease warehousing costs and increase supply chain efficiency and is therefore popular in practice. However, there is little literature quantifying the benefits of warehouse collaboration. In this paper, we study the impact of collaboration on two main internal resources of the warehouse;order pickers and dock doors. The setting we consider is relevant to multi-user warehouses, where the owner provides facilities and services to multiple clients depending on their needs. We investigate the impact of sharing the resources among the clients of such a warehouse. We present an integer linear programming (ILP) formulation, which aims at planning the order picking and shipping process while minimizing the total tardiness of shipping trucks. We use this ILP to solve the non-collaborative and collaborative case and evaluate the performance improvement resulting from the collaboration, based on operational data from a retailer. We perform computational experiments under varying warehouse configurations to investigate under what circumstances collaboration leads to the highest benefit. We find that collaboration has a significant impact on decreasing the tardiness of trucks, and the benefits mostly come from sharing the pickers rather than sharing the dock doors. We further find that the maximum benefit of collaboration is obtained at the medium-level of resource utilization. Even at low levels of utilization of a particular resource, benefits can be obtained by collaborating on complementary resources. (C) 2022 The Authors. Published by Elsevier B.V.

关键词： (T) Supply chain management Collaborative warehousing integer linear programming

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DML: Dynamic Partial Reconfiguration With Scalable Task Scheduling for Multi-Applications on FPGAs

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IEEE TRANSACTIONS ON COMPUTERS 2022年第10期71卷 2577-2591页

作者： Dhar, Ashutosh Richter, Edward Yu, Mang Zuo, Wei Wang, Xiaohao Kim, Nam Sung Chen, Deming Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

For several new applications, FPGA-based computation has shown better latency and energy efficiency compared to CPU or GPU-based solutions. We note two clear trends in FPGA-based computing. On the edge, the complexity of applications is increasing, requiring more resources than possible on today's edge FPGAs. In contrast, in the data center, FPGA sizes have increased to the point where multiple applications must be mapped to fully utilize the programmable fabric. While these limitations affect two separate domains, they both can be dealt with by using dynamic partial reconfiguration (DPR). Thus, there is a renewed interest to deploy DPR for FPGA-based hardware. In this work, we present Doing More with Less (DML) - a methodology for scheduling heterogeneous tasks across an FPGA's resources in a resource efficient manner while effectively hiding the latency of DPR. With the help of an integer linear programming (ILP) based scheduler, we demonstrate the mapping of diverse computational workloads in both cloud and edge-like scenarios. Our novel contributions include: enabling IP-level pipelining and parallelization to exploit the parallelism available within batches of work in our scheduler, and strategies to map and run multiple applications simultaneously. We consider the application of our methodology on real world benchmarks on both small (a Zedboard) and large (a ZCU106) FPGAs, across different workload batching and multiple-application scenarios. Our evaluation proves the real world efficacy of our solution, and we demonstrate an average speedup of 5X and up to 7.65X on a ZCU106 over a bulk-batching baseline via our scheduling strategies. We also demonstrate the scalablity of our scheduler by simultaneously mapping multiple applications to a single FPGA, and explore different approaches to sharing FPGA resources between applications.

关键词： Field programmable gate arrays Task analysis Pipeline processing Schedules Dynamic scheduling Runtime Processor scheduling Partial reconfiguration integer linear programming scheduling FPGA dynamic reconfiguration

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Algorithmic aspects of Roman {3}-domination in graphs

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RAIRO-OPERATIONS RESEARCH 2022年第4期56卷 2277-2291页

作者： Chakradhar, Padamutham Reddy, Palagiri Venkata Subba Natl Inst Technol Dept Comp Sci & Engn Warangal 506004 Andhra Pradesh India

Let G be a simple, undirected graph. A function g : V(G) -> {0, 1, 2, 3} having the property that Sigma(v is an element of NG(u))g(v) >= 3, if g(u) = 0, and Sigma(v is an element of NG(u))g(v) >= 2, if g(u) = 1 for any vertex u is an element of G, where N-G(u) is the set of vertices adjacent to u in G, is called a Roman {3}-dominating function (R3DF) of G. The weight of a R3DF g is the sum g(V)= Sigma(v is an element of V)g(v). The minimum weight of a R3DF is called the Roman {3}-domination number and is denoted by gamma({R3})(G). Given a graph G and a positive integer k, the Roman {3}-domination problem (R3DP) is to check whether G has a R3DF of weight at most k. In this paper, first we show that the R3DP is NP-complete for chordal graphs, planar graphs and for two subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. The minimum Roman {3}-domination problem (MR3DP) is to find a R3DF of minimum weight in the input graph. We show that MR3DP is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs. We propose a 3(1 + ln(Delta - 1))-approximation algorithm for the MR3DP, where Delta is the maximum degree of G and show that the MR3DP problem cannot be approximated within (1 - epsilon)ln|V| for any epsilon > 0 unless NP subset of DTIME(|V|(O(loglog|V|))). Next, we show that the MR3DP problem is APX-complete for graphs with maximum degree 4. We also show that the domination and Roman {3}-domination problems are not equivalent in computational complexity aspects. Finally, an ILP formulation for MR3DP is proposed.

关键词： Roman dominating function Roman {3}-domination NP-complete APX-complete integer linear programming-domination NP-complete APX-complete integer linear programming

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