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We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition.…

Data Structures and Algorithms · Computer Science 2025-06-06 Jakub Łącki , Slobodan Mitrović , Srikkanth Ramachandran , Wen-Horng Sheu

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

Machine Learning · Computer Science 2019-06-12 Yu Cheng , Ilias Diakonikolas , Rong Ge , David Woodruff

We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…

Data Structures and Algorithms · Computer Science 2017-06-27 Nikhil Bansal , Shashwat Garg , Jesper Nederlof , Nikhil Vyas

Finding Hamitonian Cycles in square grid graphs is a well studied and important questions. More recent work has extended these results to triangular and hexagonal grids, as well as further restricted versions. In this paper, we examine a…

Computational Complexity · Computer Science 2018-05-09 Kaiying Hou , Jayson Lynch

Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding…

Discrete Mathematics · Computer Science 2023-06-22 Isolde Adler , Noleen Köhler

We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, upwards of 100,000, can be sampled efficiently $\textit{in practice}$. Our algorithm incorporates constraints into the…

Machine Learning · Computer Science 2022-10-18 Yunbum Kook , Yin Tat Lee , Ruoqi Shen , Santosh S. Vempala

We revisit the algorithmic problem of finding a triangle in a graph: We give a randomized combinatorial algorithm for triangle detection in a given $n$-vertex graph with $m$ edges running in $O(n^{7/3})$ time, or alternatively in…

Data Structures and Algorithms · Computer Science 2024-03-08 Adrian Dumitrescu

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…

Discrete Mathematics · Computer Science 2020-07-03 Jorik Jooken , Pieter Leyman , Patrick De Causmaecker

Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…

Computation · Statistics 2020-08-31 Nariankadu D. Shyamalkumar , Sanvesh Srivastava

In this paper we provide sub-linear algorithms for several fundamental problems in the setting in which the input graph excludes a fixed minor, i.e., is a minor-free graph. In particular, we provide the following algorithms for minor-free…

Data Structures and Algorithms · Computer Science 2021-05-12 Reut Levi , Nadav Shoshan

We devise an algorithm that approximately computes the number of paths of length $k$ in a given directed graph with $n$ vertices up to a multiplicative error of $1 \pm \varepsilon$. Our algorithm runs in time $\varepsilon^{-2} 4^k(n+m)…

Data Structures and Algorithms · Computer Science 2018-04-26 Cornelius Brand , Holger Dell , Thore Husfeldt

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

Computation · Statistics 2017-04-19 Cheng Zhang , Babak Shahbaba , Hongkai Zhao

The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…

Data Structures and Algorithms · Computer Science 2024-08-28 Xiao Mao

In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on $n$ vertices, all…

Data Structures and Algorithms · Computer Science 2019-07-03 Serge Gaspers , Ray Li

We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in…

Computational Complexity · Computer Science 2018-09-25 Markus Bläser , Balagopal Komarath , Karteek Sreenivasaiah

The cycle space of a graph $G$, denoted $C(G)$, is a vector space over ${\mathbb F}_2$, spanned by all incidence vectors of edge-sets of cycles of $G$. If $G$ has $n$ vertices, then $C_n(G)$ denotes the subspace of $C(G)$, spanned by the…

Combinatorics · Mathematics 2025-07-08 Dan Hefetz , Michael Krivelevich

The problem of the reconstruction of the large scale density and velocity fields from peculiar velocities surveys is addressed here within a Bayesian framework by means of Hamiltonian Monte Carlo (HMC) sampling. The HAmiltonian Monte carlo…

Cosmology and Nongalactic Astrophysics · Physics 2022-06-01 Aurélien Valade , Yehuda Hoffman , Noam I Libeskind , Romain Graziani

In Bayesian inference, Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm known for its efficiency in sampling from complex probability distributions. However, its application to models with latent…

Computation · Statistics 2025-04-15 Alaa Amri , Víctor Elvira , Amy L. Wilson

We prove that Hamiltonicity in maximum-degree-3 grid graphs (directed or undirected) is ASP-complete, i.e., it has a parsimonious reduction from every NP search problem (including a polynomial-time bijection between solutions). As a…

Computational Complexity · Computer Science 2026-05-05 MIT Hardness Group , Josh Brunner , Lily Chung , Erik D. Demaine , Jenny Diomidova , Della Hendrickson , Andy Tockman

Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…

Data Structures and Algorithms · Computer Science 2022-12-15 Jun Kawahara , Toshiki Saitoh , Hirokazu Takeda , Ryo Yoshinaka , Yui Yoshioka