Index coding, a source coding problem over broadcast channels, has been a subject of both theoretical and practical interests since its introduction (by Birk and Kol, 1998). In short, the problem can be defined as fol...
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Index coding, a source coding problem over broadcast channels, has been a subject of both theoretical and practical interests since its introduction (by Birk and Kol, 1998). In short, the problem can be defined as follows: there is an input P (sic) (p(1), ..., p(n)), a set of n clients who each desire a single entry p(i) of the input, and a broadcaster whose goal is to send as few messages as possible to all clients so that each one can recover its desired entry. Additionally, each client has some predetermined "side information," corresponding to the certain entries of the input P, which we represent as the "side information graph" G. The graph G has a vertex v(i) for client i and a directed edge (v(i), v(j)), indicating that client i knows the jth entry of the input. Given a fixed side information graph G, we are interested in determining or approximating the "broadcast rate" of index coding on the graph, i.e., the least number of messages the broadcaster can transmit so that every client recovers its desired information. The complexity of determining this broadcast rate in the most general case is open, and the best-known approximations are barely better than the trivial O(n)-approximation corresponding to sending each client their information directly without performing any coding. Using index coding schemes based on linear programs (LPs), we take a two-pronged approach to approximating the broadcast rate. First, extending earlier work on planar graphs, we focus on approximating the broadcast rate for special graph families, such as graphs with the small chromatic number and disk graphs. In certain cases, we are able to show that simple LP-based schemes give constant-factor approximations of the broadcast rate, which seem extremely difficult to obtain in the general case. Second, we provide several LP-based schemes for the general case, which are not constant-factor approximations, but which strictly improve on the best-known schemes. These can be viewed as both
This paper proposes a new full-Newton step infeasible interior-point algorithm based on a kernel function with linear growth terms for a linear programming. This kernel function determines search directions and the pr...
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Singh et al. [1], for solving the fully neutrosophic linear programming problems stated that the method of Abdel-Basset et al. [2] is scientifically incorrect and suggested a modified version for it. They have constru...
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The objective of this paper is to study the linear programming algorithm of the mathematical model of agricultural machinery allocation when there are many farmland projects and cross operations. In this paper, combin...
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The objective of this paper is to study the linear programming algorithm of the mathematical model of agricultural machinery allocation when there are many farmland projects and cross operations. In this paper, combined with the mechanization process of crops in XPCC, the linear programming algorithm of mathematical model was used to establish the allocation scheme of different scales. All equations were solved and analyzed, and the allocation schemes of different planting scales were compared. It is also observed that through the interactive conflicts in between multiple objectives a solution vector can be analyzed. The results show that the activity cost of Scheme 5 was the lowest, only 1,260 yuan per mu, which was the best way to equip agricultural machinery. The results present that it is of great significance to optimize the configuration of agricultural machinery. The experimental results present that the portion of water which is reused in comparison with the total water is gradually increasing which leads to the overall reduction in water consumption.
The aim of this paper is to introduce a simplified presentation of a new computing procedure for solving trapezoidal neutrosophic linear programming (TrNLP) problem under uncertainties. Therefore, we firstly define th...
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The neutrosophic mathematical linear programming in its duality fashion is originally exhibited in this manuscript. In accordance with this concept, the relationship of the duality between the neutrosophic objective f...
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A single-valued neutrosophic set, an generalization of intuitionistic fuzzy set, is a powerful model to deal with uncertainty. In this study we present a method to solve LR-type single-valued neutrosophic linear progr...
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For a constrained optimal impulse control problem of an abstract dynamical system, we introduce the occupation measures along with the aggregated occupation measures and present two associated linear programs. We prov...
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For a constrained optimal impulse control problem of an abstract dynamical system, we introduce the occupation measures along with the aggregated occupation measures and present two associated linear programs. We prove that the two linear programs are equivalent under appropriate conditions, and each linear program gives rise to an optimal strategy in the original impulse control problem. In particular, we show the absence of the relaxation gap. By means of an example, we also present a detailed comparison of the occupation measures and linear programs introduced here with the related notions in the literature. (C) 2021 Elsevier Inc. All rights reserved.
In this paper, the triangular fuzzy bilevel programming problem (TFBLPP) is investigated. We transformed TBFLPP to interval fuzzy bilevel linear programming problem by using nearest interval approximation. In the next...
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