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Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of Mixed-Integer Programming solvers. In its full form, SB evaluates all variables to branch on and…

Optimization and Control · Mathematics 2024-04-08 Gioni Mexi , Somayeh Shamsi , Mathieu Besançon , Pierre Le Bodic

A {\em strong $k$-edge-coloring} of a graph $G$ is a mapping from $E(G)$ to $\{1,2,\ldots,k\}$ such that every two adjacent edges or two edges adjacent to the same edge receive distinct colors. The {\em strong chromatic index} $\chi_s'(G)$…

Combinatorics · Mathematics 2018-01-24 Ilkyoo Choi , Jaehoon Kim , Alexandr V. Kostochka , André Raspaud

Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…

Combinatorics · Mathematics 2021-03-05 Ewan Davies , Matthew Jenssen , Will Perkins , Barnaby Roberts

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

Machine Learning · Computer Science 2025-08-22 Soumya Sarkar , Shweta Jain

Stochastic Gumbel graph networks are proposed to learn high-dimensional time series, where the observed dimensions are often spatially correlated. To that end, the observed randomness and spatial-correlations are captured by learning the…

Machine Learning · Computer Science 2023-07-13 Jin Guo , Ting Gao , Yufu Lan , Peng Zhang , Sikun Yang , Jinqiao Duan

A $(q,r)$\emph{-tree-coloring} of a graph $G$ is a $q$-coloring of vertices of $G$ such that the subgraph induced by each color class is a forest of maximum degree at most $r.$ An \emph{equitable $(q, r)$-tree-coloring} of a graph $G$ is a…

Combinatorics · Mathematics 2015-06-15 Keaitsuda Maneeruk Nakprasit , Kittikorn Nakprasit

In order to achieve maximal stop mixing and m_h=125 GeV, we consider extensions of minimal GMSB that include marginal MSSM-messenger superpotential interactions. Using a new approach to analytic continuation in superspace, we derive general…

High Energy Physics - Phenomenology · Physics 2015-06-15 Jared A. Evans , David Shih

A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…

Probability · Mathematics 2025-07-22 Jason Gaitonde , Elchanan Mossel

We study the problem of constructing a (near) random proper $q$-colouring of a simple k-uniform hypergraph with n vertices and maximum degree \Delta. (Proper in that no edge is mono-coloured and simple in that two edges have maximum…

Discrete Mathematics · Computer Science 2009-01-26 Alan Frieze , Pall Melsted

Recent developments in approximate counting have made startling progress in developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections to…

Computational Complexity · Computer Science 2022-08-23 Andreas Galanis , Heng Guo , Jiaheng Wang

A graph is weakly $2$-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-19 Alkida Balliu , Juho Hirvonen , Dennis Olivetti , Jukka Suomela

We describe a new method for measuring the true redshift distribution of any set of objects studied only photometrically. The angular cross-correlation between objects in a photometric sample with objects in some spectroscopic sample as a…

Astrophysics · Physics 2009-11-13 Jeffrey A. Newman

In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-03-15 Nicolas Bousquet , Louis Esperet , François Pirot

An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T) is related to the maximum…

Combinatorics · Mathematics 2007-05-23 Bryan L. Shader , In-Jae Kim

Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a non-convex high-dimensional…

Machine Learning · Statistics 2022-06-08 Song Mei , Andrea Montanari , Phan-Minh Nguyen

Let $G=G(n,m)$ be a random graph whose average degree $d=2m/n$ is below the $k$-colorability threshold. If we sample a $k$-coloring $\sigma$ of $G$ uniformly at random, what can we say about the correlations between the colors assigned to…

Combinatorics · Mathematics 2015-01-27 Amin Coja-Oghlan , Charilaos Efthymiou , Nor Jaafari

Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from…

Machine Learning · Computer Science 2026-03-20 Kaiyang Li , Shihao Ji , Zhipeng Cai , Wei Li

A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…

Computer Vision and Pattern Recognition · Computer Science 2010-10-22 Guoshen Yu , Guillermo Sapiro

Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…

Computational Complexity · Computer Science 2016-04-07 Yi-Jun Chang , Tsvi Kopelowitz , Seth Pettie

Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…

Combinatorics · Mathematics 2024-07-26 Nathan Albin , Kapila Kottegoda , Pietro Poggi-Corradini