The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in the complete graphs, there exists...
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Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Lapl...
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ISBN:
(数字)9798350368741
ISBN:
(纸本)9798350368758
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node i, to determine its polarity β i ∈{−1,1} and edge weights $\left\{ {{w_{i,j}}} \right\}_{j = 1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce "consistent" signs of edge weights $\left\{ {{w_{i,j}}} \right\}_{j = 1}^N$ with the polarities of connected nodes—i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adopt projections on convex set (POCS) to determine a suitable CLIME parameter ρ > 0 that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph neural networks designed for positive graphs on balanced signed graphs.
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to e...
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We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute these quantities using dynamic and linear programming.
The research on cargo volume forecasting and manpower demand involves utilizing appropriate models and algorithms to predict future information based on historical cargo volume and personnel allocation data, thereby e...
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ISBN:
(数字)9798350389579
ISBN:
(纸本)9798350389586
The research on cargo volume forecasting and manpower demand involves utilizing appropriate models and algorithms to predict future information based on historical cargo volume and personnel allocation data, thereby enhancing resource optimization and driving development. After preprocessing the data provided by a certain enterprise, this study utilizes LSTM (Long Short-Term Memory) patterns with reference to the daily cargo volume of each sorting center over the past four months and the hourly cargo volume over the past 30 days. A stationary time series model is constructed, and LSTM neural network parameters are set. Through rolling forecasts conducted via Python programs, an effective prediction of the hourly cargo volume for each of the 57 sorting centers over the next 30 days is achieved. Subsequently, a linear programming model is established to determine the objective function for maximizing personnel arrangement efficiency. Constraints such as single-shift attendance and employee headcount limits are selected. The Branch and Bound algorithm is employed to initialize upper and lower bounds and determine the feasible space, effectively yielding personnel deployment plans for different time periods at each sorting center over the next 30 days. The forecasting methods and data obtained in this paper play a significant role in resource allocation and service quality improvement in related industries.
Integer linear programming (ILP) is an NP-complete combinatorial optimization problem (COP), suggesting that it is computationally challenging to solve due to its exponentially increased operations with scaling. As sh...
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ISBN:
(数字)9798350394061
ISBN:
(纸本)9798350394078
Integer linear programming (ILP) is an NP-complete combinatorial optimization problem (COP), suggesting that it is computationally challenging to solve due to its exponentially increased operations with scaling. As shown in Fig. 1, The ILP is relevant in various real-world scenarios such as computational biology [1], investment decision, automated driving, and electronic design automation [2]. An ILP solver aims to find a set of integer variables
$(x)$
to maximize a linear objective function
$(c\cdot x)$
, subject to a set of linear constraints
$(A\cdot x\leq b)$
. With the increasingly wide usage of ILP, various new solving algorithms [3] have been proposed, but the performance are limited by substantial memory access. ILP coefficients are fixed during solving, but software solvers on cache-register architectures frequently access cache to reload coefficients because of small register file size, causing up to a
$10^{14}\mathrm{x}$
disparity between stored and accessed memory bits. FPGA [4] and AISC [5] accelerated solvers improve the speed by customized processing element (PE), but they still need frequent accesses to Block-RAM or scratch pad. Compute-in-memory (CIM) solutions are well-suited for ILP solving which has extremely high data reuse, but existing CIM DNN accelerators incur precision loss with hardware tradeoffs, which is unacceptable for ILP where the feasibility checking must be correct. Previous all-digital CIM COP solver for Boolean variables [6] uses a customized
$6\mathrm{T}$
-6T{###}
$3\mathrm{T}$
cell, limiting their adaptability to different technologies.
MSC Codes 52C17, 11H31The Tammes problem delves into the optimal arrangement of N points on the surface of the n-dimensional unit sphere (denoted as Sn−1), aiming to maximize the minimum distance between any two point...
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Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few app...
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In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term "generalized optimal partial tra...
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We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to ap...
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