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We present a general strategy to extend quantum cluster algorithms for S=1/2 spin systems, such as the loop algorithm, to systems with arbitrary size of spins. In general, the partition function of a high-S spin system is represented in…

Statistical Mechanics · Physics 2009-10-31 Synge Todo , Kiyoshi Kato

The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is state space explosion problem. To address this issue,…

Logic in Computer Science · Computer Science 2023-08-08 Mohammadsadegh Mohaghegh , Khayyam Salehi

In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…

Data Structures and Algorithms · Computer Science 2015-12-10 Stephan Beyer , Markus Chimani

Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…

Data Structures and Algorithms · Computer Science 2023-07-27 Antares Chen , Lorenzo Orecchia , Erasmo Tani

The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…

Condensed Matter · Physics 2009-10-28 G. Paladin , M. Serva

We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…

Discrete Mathematics · Computer Science 2019-02-22 Tobias Friedrich , Andreas Göbel , Frank Neumann , Francesco Quinzan , Ralf Rothenberger

We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…

Optimization and Control · Mathematics 2025-06-09 Keita Kume , Isao Yamada

We extend the stochastic GW (sGW) formalism to fully spin-polarized systems, encompassing both collinear and non-collinear spin configurations. For non-collinear systems-where Kohn-Sham states are complex two-component spinors-we develop a…

Materials Science · Physics 2025-09-26 Xuance Jiang , Vojtech Vlcek

In the Strip Packing problem (SP), we are given a vertical half-strip $[0,W]\times[0,\infty)$ and a set of $n$ axis-aligned rectangles of width at most $W$. The goal is to find a non-overlapping packing of all rectangles into the strip such…

Data Structures and Algorithms · Computer Science 2022-05-09 Arindam Khan , Aditya Lonkar , Arnab Maiti , Amatya Sharma , Andreas Wiese

We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…

Data Structures and Algorithms · Computer Science 2025-05-29 Christoph Hunkenschröder , Martin Koutecký , Asaf Levin , Tung Anh Vu

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Data Structures and Algorithms · Computer Science 2013-09-25 Vincent Blondel , Kyomin Jung , Pushmeet Kohli , Devavrat Shah

In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists…

Optimization and Control · Mathematics 2025-03-18 Deren Han , Min Tao , Zihao Xia

Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…

Numerical Analysis · Mathematics 2024-07-30 Nicolas Boullé , Astrid Herremans , Daan Huybrechs

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

Machine Learning · Statistics 2021-08-23 Patrick Héas , Cédric Herzet

We consider the computational problem of finding short paths in the skeleton of the perfect matching polytope of a bipartite graph. We prove that unless $P=NP$, there is no polynomial-time algorithm that computes a path of constant length…

Optimization and Control · Mathematics 2022-10-27 Jean Cardinal , Raphael Steiner

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006) allows to express the exact partition function of a graphical model as a…

Artificial Intelligence · Computer Science 2009-05-25 V. Gómez , H. J. Kappen , M. Chertkov

For a polynomial f: {-1, 1}^n --> C, we define the partition function as the average of e^{lambda f(x)} over all points x in {-1, 1}^n, where lambda in C is a parameter. We present a quasi-polynomial algorithm, which, given such f, lambda…

Data Structures and Algorithms · Computer Science 2016-11-30 Alexander Barvinok

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…

Optimization and Control · Mathematics 2014-04-23 Mojtaba Kadkhodaie , Maziar Sanjabi , Zhi-Quan Luo

Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-19 Mu Li , Dave G. Andersen , Alexander J. Smola

Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their…

Data Structures and Algorithms · Computer Science 2015-09-21 Pinyan Lu , Kuan Yang , Chihao Zhang