Related papers: Polynomial-time approximation algorithms for the a…
Partition functions are an important research object in combinatorics and mathematical physics [Barvinok, 2016]. In this work, we consider the partition function of the Ising antiferromagnet on random regular graphs and characterize its…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal…
We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D…
Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…
We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an…
We present an algorithm to approximate partition functions of 3-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by…
The Marcus-Spielman-Srivastava theorem (Annals of Mathematics, 2015) for the Kadison-Singer conjecture implies the following result in spectral graph theory: For any undirected graph $G = (V,E)$ with a maximum edge effective resistance at…
In recent decades, a number of profound theorems concerning approximation of hard counting problems have appeared. These include estimation of the permanent, estimating the volume of a convex polyhedron, and counting (approximately) the…
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…
We consider graphs with two communities and analyze an algorithm for learning the community labels when the edges of the graph and only a small fraction of the labels are known in advance. The algorithm is based on the Glauber dynamics for…
We present a polynomial-time $(\alpha_{GW} + \varepsilon)$-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where $\alpha_{GW} \approx 0.878$ is the approximation guarantee of the Goemans-Williamson…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
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…
We prove optimality of the Arf invariant formula for the generating function of even subgraphs, or, equivalently, the Ising partition function, of a graph.
The Ising antiferromagnet is an important statistical physics model with close connections to the {\sc Max Cut} problem. Combining spatial mixing arguments with the method of moments and the interpolation method, we pinpoint the replica…
A stochastic incremental subgradient algorithm for the minimization of a sum of convex functions is introduced. The method sequentially uses partial subgradient information and the sequence of partial subgradients is determined by a general…