A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation has generated considerable interest, motivating eff...
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ISBN:
(纸本)9783030589424;9783030589417
A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation has generated considerable interest, motivating efforts to design efficient and adroit minor-embedding procedures that bypass sparsity constraints. In this paper, starting from a previous equational formulation by Dridi et al. (arXiv:1810.01440), we propose integer programming (IP) techniques for solving the minor-embedding problem. The first approach involves a direct translation from the previous equational formulation to IP, while the second decomposes the problem into an assignment master problem and fiber condition checking subproblems. The proposed methods are able to detect instance infeasibility and provide bounds on solution quality, capabilities not offered by currently employed heuristic methods. We demonstrate the efficacy of our methods with an extensive computational assessment involving three families of random graphs of varying sizes and densities. The direct translation as a monolithic IP model can be solved with existing commercial solvers yielding valid minor-embeddings but it is outperformed, overall, by the decomposition approach. Our results demonstrate the promise of our methods for the studied benchmarks, highlighting the advantages of using IP technology for minor-embedding problems.
The lack of façade structures in photogrammetric mesh models renders them inadequate for meeting the demands of intricate applications. Moreover, these mesh models exhibit irregular surfaces with considerable geo...
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Preserving privacy is one of the fundamental requirements of firms that share data with their business partners for building advanced data mining models. Firms often aim to protect the disclosure of sensitive knowledg...
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Preserving privacy is one of the fundamental requirements of firms that share data with their business partners for building advanced data mining models. Firms often aim to protect the disclosure of sensitive knowledge or information discovered during the data mining process. In this study, we investigate the problem of Frequent Itemset Hiding (FIH) which aims to hide sensitive itemset relationships present in a transactional database. We propose a two-stage integer programming model that maximizes the proportion of unaltered transactions in the sanitized database and protects sensitive itemset relationships. The model exploits the concept of transactional equivalence and significantly reduces the size of the FIH problem. In addition, our model enables the identification of solutions with minimal side effects. We conduct an experimental evaluation on both real and synthetic databases to show that our approach is scalable and produces a sanitized database with maximum accuracy. The generated solution is also found to have lower side effects (itemset information loss) compared to other state-of-the-art methods. Our experiments on very large problem instances show problem size reductions of one to three orders of magnitude. The proposed approach is quite attractive and practically useful for solving large-scale FIH problem instances and preserving privacy in increasingly shared and big data-driven organizational environments.
Puzzles and games have been played over years. Every kind of puzzle has its own logic and mathematics. Some decisional notions might become clearer when we were able to understand the science underlying them and model...
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A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with dual tree-depth d and largest entry Delta are ...
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A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with dual tree-depth d and largest entry Delta are solvable in time g(d, Delta)poly(n) for some function g. However, the dual tree-depth of a constraint matrix is not preserved by row operations, i.e., a given integer program can be equivalent to another with a smaller dual tree-depth, and thus does not reflect its geometric structure. We prove that the minimum dual tree-depth of a row-equivalent matrix is equal to the branch-depth of the matroid defined by the columns of the matrix. We design a fixed parameter algorithm for computing branch-depth of matroids represented over a finite field and a fixed parameter algorithm for computing a row-equivalent matrix with minimum dual treedepth. Finally, we use these results to obtain an algorithm for integer programming running in time g(d\ast, \Delta)poly(n) where d\ast is the branch-depth of the constraint matrix;the branch-depth cannot be replaced by the more permissive notion of branch-width.
Team-based learning (TBL) plays a significant role in many organizational settings, necessitating a sophisticated and comprehensive approach to team formation. This study introduces an innovative application of multi-...
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Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all common activations, value functions o...
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A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linea...
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Energy storage systems-in particular, Pumped Hydropower Storage (PHS)-will be increasingly important to support the transition of power systems toward zero emissions. The reason is that PHS can mitigate the variabilit...
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Energy storage systems-in particular, Pumped Hydropower Storage (PHS)-will be increasingly important to support the transition of power systems toward zero emissions. The reason is that PHS can mitigate the variability and uncertainty of renewable energy production from solar and wind power to balance electricity demand with supply. In this paper, we propose an integer programming problem for PHS siting that uses a Digital Elevation Model (DEM) to meet an energy storage requirement. It assumes the existence of a reservoir, lake, or river, and decides where to build a reservoir that will constitute the PHS with the existing body of water. This model finds minimum-cost project candidates given parameters such as desired head, power, and operation time. The paper discusses different solution methods to assure reservoir closure and avoid its fragmentation. A heuristic explores the representations of the DEM, from more aggregate to more precise, to sequentially refine the solution based on the last selected site, which reduces computational effort. The formulation is general and the objective function includes both construction and equipment costs. Constraints are related to the energy storage target and reservoir closure based on the DEM. We illustrate the methodology by selecting multiple PHS projects next to the reservoir of the Sobradinho hydropower plant in Brazil. The result of this model can be seen as a bottom-up step that prepares PHS candidate projects to be considered by an integrated resource planning model in a top-down step, that would select from these shortlisted projects.
We consider 4-block n-fold integer programming, which can be written as max{w.x : Hx = b, l <= x <= u, x is an element of Z(N)}, where the constraint matrix H is composed of small matrices A, B, C, D such that t...
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We consider 4-block n-fold integer programming, which can be written as max{w.x : Hx = b, l <= x <= u, x is an element of Z(N)}, where the constraint matrix H is composed of small matrices A, B, C, D such that the first row of H is (C, D, D, ..., D), the first column of H is (C, B, B, ..., B), the main diagonal of H is (C, A, A, ..., A), and all the other entries are 0. There are n copies of D, B, and A. The special case where B = C = 0 is known as n-fold integer programming. Prior algorithmic results for 4-block n-fold integer programming and its special cases usually take Delta, the largest absolute value among entries of H, as part of the parameters. In this paper, we explore the possibility of solving the problems polynomially when the number of rows and columns of the small matrices are constant. We show that, assuming P not equal NP, this is not possible even if A = (1, 1, Delta) and B = C = 0. However, this becomes possible if A = (1, ..., 1) or A is an element of Z(1x2), or more generally if A is an element of Z(sAxtA), t(A) = s(A) + 1 and the rank of matrix A satisfies that rank(A) = s(A). (C) 2022 Elsevier B.V. All rights reserved.
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