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A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order…

Numerical Analysis · Mathematics 2022-06-10 Chongmin Song , Sascha Eisenträger

In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two…

Quantum Physics · Physics 2009-11-10 Maarten Van den Nest , Jeroen Dehaene , Bart De Moor

We develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the…

Data Structures and Algorithms · Computer Science 2018-02-13 Anatoly D. Plotnikov

We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth…

Data Structures and Algorithms · Computer Science 2016-04-21 Fedor V. Fomin , Daniel Lokshtanov , Dániel Marx , Marcin Pilipczuk , Michał Pilipczuk , Saket Saurabh

We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…

Computational Complexity · Computer Science 2013-01-07 Adam Klivans , Raghu Meka

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…

Optimization and Control · Mathematics 2015-05-14 Raymond Hemmecke , Matthias Köppe , Robert Weismantel

Given a family F of subsets of a ground set V, its orthogonal is defined to be the family of subsets that do not overlap any element of F. Using this tool we revisit the problem of designing a simple linear time algorithm for undirected…

Discrete Mathematics · Computer Science 2010-06-29 Pierre Charbit , Fabien de Montgolfier , Mathieu Raffinot

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\GL_{1}$ and $\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present…

Number Theory · Mathematics 2014-11-18 Philippe Michel , Akshay Venkatesh

We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…

Data Structures and Algorithms · Computer Science 2016-10-26 Dániel Marx , Marcin Pilipczuk

The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…

Computational Complexity · Computer Science 2019-02-20 Manuel Arora , Gábor Ivanyos , Marek Karpinski , Nitin Saxena

Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide…

Methodology · Statistics 2024-05-27 Victoria Volodina , Nikki Sonenberg , Peter Challenor , Jim Q. Smith

A directed multigraph is said vulnerable if it can generate Braess paradox in Traffic Networks. In this paper, we give a graph-theoretic characterisation of vulnerable directed multigraphs; analogous results appeared in the literature only…

Data Structures and Algorithms · Computer Science 2024-05-24 Pietro Cenciarelli , Daniele Gorla , Ivano Salvo

We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our…

Combinatorics · Mathematics 2009-06-02 Kevin Byrnes

We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…

Artificial Intelligence · Computer Science 2015-08-19 Paul Swoboda , Alexander Shekhovtsov , Jörg Hendrik Kappes , Christoph Schnörr , Bogdan Savchynskyy

We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential…

Numerical Analysis · Mathematics 2026-03-16 Nicolas Gillis , Carmela Scalone

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…

Signal Processing · Electrical Eng. & Systems 2020-02-18 Bo Jiang , Ashkan Panahi , Hamid Krim , Yiyi Yu , Spencer L. Smith

We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and…

Data Structures and Algorithms · Computer Science 2018-04-04 Zeyuan Allen-Zhu , Ankit Garg , Yuanzhi Li , Rafael Oliveira , Avi Wigderson

The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph $G$ and a parameter $k$, one has to decide if there is a set $S$ of at most $k$ vertices such that $G-S$ is acyclic. Assuming the…

Data Structures and Algorithms · Computer Science 2026-01-16 Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system…

Machine Learning · Statistics 2018-08-03 Federico Tomasi , Veronica Tozzo , Saverio Salzo , Alessandro Verri

We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-30 Tianyu Liang , Chao Chen , Yotam Yaniv , Hengrui Luo , David Tench , Xiaoye S. Li , Aydin Buluc , James Demmel