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In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…

Statistics Theory · Mathematics 2025-05-28 Rushil Mallarapu , Mark Sellke

We consider the problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment of jobs to machines, to minimize the expected value of the maximum load over all the machines. For…

Data Structures and Algorithms · Computer Science 2019-04-17 Anupam Gupta , Amit Kumar , Viswanath Nagarajan , Xiangkun Shen

We revisit the classic Pandora's Box (PB) problem under correlated distributions on the box values. Recent work of arXiv:1911.01632 obtained constant approximate algorithms for a restricted class of policies for the problem that visit boxes…

Data Structures and Algorithms · Computer Science 2023-07-25 Shuchi Chawla , Evangelia Gergatsouli , Jeremy McMahan , Christos Tzamos

We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a…

Combinatorics · Mathematics 2022-12-09 Juanjo Rué , Maximilian Wötzel

Robust principal component analysis is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and $\ell_0$-norm of matrices. In this paper, we study the rank and $\ell_0$…

Optimization and Control · Mathematics 2026-03-04 Wenjing Li , Wei Bian , Kim-Chuan Toh

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…

Computational Complexity · Computer Science 2007-05-23 Harry B. Hunt , Madhav V. Marathe , Venkatesh Radhakrishnan , Richard E. Stearns

This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…

Data Structures and Algorithms · Computer Science 2020-03-10 Feras A. Saad , Cameron E. Freer , Martin C. Rinard , Vikash K. Mansinghka

We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…

Machine Learning · Computer Science 2012-05-14 Shankar Vembu , Thomas Gartner , Mario Boley

Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

Computation · Statistics 2018-04-12 Christian P. Robert , Victor Elvira , Nick Tawn , Changye Wu

Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…

Machine Learning · Computer Science 2017-08-08 Paul M. B. Vitanyi , Nick Chater

General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…

High Energy Physics - Lattice · Physics 2021-11-24 Luigi Del Debbio , Joe Marsh Rossney , Michael Wilson

We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…

Data Structures and Algorithms · Computer Science 2023-01-02 Jakub Łącki , Vahab Mirrokni , Christian Sohler

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…

Machine Learning · Computer Science 2013-11-08 Moshe Dubiner , Matan Gavish , Yoram Singer

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…

Machine Learning · Statistics 2012-11-21 A. Gokcen Mahmutoglu , Alper T. Erdogan , Alper Demir

We study the worst-case communication complexity of distributed algorithms computing a path problem based on stationary distributions of random walks in a network $G$ with the caveat that $G$ is also the communication network. The problem…

Data Structures and Algorithms · Computer Science 2008-10-30 Rahul Sami , Andy Twigg

One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix…

Statistics Theory · Mathematics 2024-04-26 Muhammad Usman Farooq , Tobias Fritz , Erkka Haapasalo , Marco Tomamichel

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

We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability…

Other Condensed Matter · Physics 2007-05-23 Yaniv S. Avizrats , Joshua Feinberg , Shmuel Fishman

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…

Data Structures and Algorithms · Computer Science 2020-09-07 Isabel Beichl , Alathea Jensen

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane