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We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…

Data Structures and Algorithms · Computer Science 2025-11-11 Gautam Chandrasekaran , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We investigate the use of a Hamiltonian Monte Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte Carlo (MCMC) methods, such as Metropolis-Hastings MCMC, have been…

General Relativity and Quantum Cosmology · Physics 2019-08-19 Edward K. Porter , Jérôme Carré

We design the first efficient sensitivity oracles and dynamic algorithms for a variety of parameterized problems. Our main approach is to modify the algebraic coding technique from static parameterized algorithm design, which had not…

Data Structures and Algorithms · Computer Science 2022-06-22 Josh Alman , Dean Hirsch

Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have…

Data Structures and Algorithms · Computer Science 2018-12-18 Yin Tat Lee , Zhao Song , Santosh S. Vempala

We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…

Data Structures and Algorithms · Computer Science 2010-01-07 Frederic Dorn , Fedor V. Fomin , Daniel Lokshtanov , Venkatesh Raman , Saket Saurabh

Since counting subgraphs in general graphs is, by and large, a computationally demanding problem, it is natural to try and design fast algorithms for restricted families of graphs. One such family that has been extensively studied is that…

Data Structures and Algorithms · Computer Science 2022-08-29 Lior Gishboliner , Yevgeny Levanzov , Asaf Shapira , Raphael Yuster

In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…

Data Structures and Algorithms · Computer Science 2016-11-03 Michael B. Cohen , Jon Kelner , John Peebles , Richard Peng , Aaron Sidford , Adrian Vladu

We provide a deterministic $\tilde{O}(\log N)$-space algorithm for estimating random walk probabilities on undirected graphs, and more generally Eulerian directed graphs, to within inverse polynomial additive error…

Computational Complexity · Computer Science 2022-03-14 AmirMahdi Ahmadinejad , Jonathan Kelner , Jack Murtagh , John Peebles , Aaron Sidford , Salil Vadhan

In this note, we study the emergence of Hamiltonian Berge cycles in random $r$-uniform hypergraphs. For $r\geq 3$, we prove an optimal stopping-time result that if edges are sequently added to an initially empty $r$-graph, then as soon as…

Combinatorics · Mathematics 2021-07-01 Deepak Bal , Ross Berkowitz , Pat Devlin , Mathias Schacht

A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…

Data Structures and Algorithms · Computer Science 2013-01-16 Dmitriy Nuriyev

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

Computation · Statistics 2019-10-15 Babak Shahbaba , Luis Martinez Lomeli , Tian Chen , Shiwei Lan

In the standard random graph process, edges are added to an initially empty graph one by one uniformly at random. A classic result by Ajtai, Koml\'os, and Szemer\'edi, and independently by Bollob\'as, states that in the standard random…

Combinatorics · Mathematics 2026-03-24 Seonghyuk Im , Minseo Kim

Cartesian products of graphs and hypergraphs have been studied since the 1960s. For (un)directed hypergraphs, unique \emph{prime factor decomposition (PFD)} results with respect to the Cartesian product are known. However, there is still a…

Discrete Mathematics · Computer Science 2015-08-31 Marc Hellmuth , Florian Lehner

Given a bipartite graph, the maximum balanced biclique (\textsf{MBB}) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has…

Data Structures and Algorithms · Computer Science 2020-07-20 Lu Chen , Chengfei Liu , Rui Zhou , Jiajie Xu , Jianxin Li

For $0\leq \ell <k$, a Hamiltonian $\ell$-cycle in a $k$-uniform hypergraph $H$ is a cyclic ordering of the vertices of $H$ in which the edges are segments of length $k$ and every two consecutive edges overlap in exactly $\ell$ vertices. We…

Combinatorics · Mathematics 2021-11-01 Asaf Ferber , Liam Hardiman , Adva Mond

Many applications require randomly sampling bipartite graphs with fixed degrees, or randomly sampling incidence matrices with fixed row and column sums. Although several sampling algorithms exist, the ``curveball'' algorithm is the most…

Data Structures and Algorithms · Computer Science 2022-11-01 Karl Godard , Zachary P. Neal

Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…

Methodology · Statistics 2015-02-02 Lotfi Chaari , Jean-Yves Tourneret , Caroline Chaux , Hadj Batatia

The Transversal problem, i.e, the enumeration of all the minimal transversals of a hypergraph in output-polynomial time, i.e, in time polynomial in its size and the cumulated size of all its minimal transversals, is a fifty years old open…

Data Structures and Algorithms · Computer Science 2014-07-09 Mamadou Moustapha Kanté , Vincent Limouzy , Arnaud Mary , Lhouari Nourine , Takeaki Uno

We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that…

Probability · Mathematics 2023-09-20 Julia Gaudio , Miklós Z. Rácz , Anirudh Sridhar

We show for an arbitrary $\ell_p$ norm that the property that a random geometric graph $\mathcal G(n,r)$ contains a Hamiltonian cycle exhibits a sharp threshold at $r=r(n)=\sqrt{\frac{\log n}{\alpha_p n}}$, where $\alpha_p$ is the area of…

Discrete Mathematics · Computer Science 2007-05-23 J. Diaz , D. Mitsche , X. Perez