相关论文: Entropy-based analysis of the number partitioning …

We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with…

The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…

Deep Neural Networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. Many different algorithms have been proposed to implement the most computationally expensive layers of…

Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a…

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…

The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…

The decoding problem is a ubiquitous algorithmic task in fault-tolerant quantum computing, and solving it efficiently is essential for scalable quantum computing. Here, we prove that minimum-weight decoding is NP-hard in three…

We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this…

We present a ${\Gamma}$-convergence approximation for the total anisotropic length of a partition. This theoretical result gives rise to a numerical method which allows the study of minimal partitions with respect to different anisotropies.…

We discuss a variant of multitask n-vehicle exploration problem. Instead of requiring an optimal permutation of vehicles in every group, the new problem asks all vehicles in a group to arrive at a same destination. It can also be viewed as…

The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a…

Most existing classification methods aim to minimize the overall misclassification error rate. However, in applications such as loan default prediction, different types of errors can have varying consequences. To address this asymmetry…

We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…

Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…

A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…

For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…

We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…

The Classical-map Hyper-Netted-Chain (CHNC) technique is a simple method of calculating quantum pair-distribution functions, spin-dependent energies, etc., of strongly-interacting {\it uniform} systems. We present CHNC calculations of…