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Distributed matrix computations -- matrix-matrix or matrix-vector multiplications -- are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in…

Information Theory · Computer Science 2020-06-03 Anindya B. Das , Aditya Ramamoorthy , Namrata Vaswani

This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…

Information Theory · Computer Science 2007-11-08 Igal Sason , Gil Wiechman

We analyze sequences generated by interior point methods (IPMs) in convex and nonconvex settings. We prove that moving the primal feasibility at the same rate as the barrier parameter $\mu$ ensures the Lagrange multiplier sequence remains…

Optimization and Control · Mathematics 2019-06-13 Gabriel Haeser , Oliver Hinder , Yinyu Ye

We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…

Computational Complexity · Computer Science 2021-02-18 Vincent Cohen-Addad , Éric Colin de Verdière , Daniel Marx , Arnaud de Mesmay

We consider the ``minimum degree spanning tree'' problem. As input, we receive an undirected, connected graph $G=(V, E)$ with $n$ nodes and $m$ edges, and our task is to find a spanning tree $T$ of $G$ that minimizes $\max_{u \in V}…

Data Structures and Algorithms · Computer Science 2026-03-02 Sayan Bhattacharya , Ermiya Farokhnejad , Haoze Wang

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…

Combinatorics · Mathematics 2007-05-23 Jaroslav Nesetril , Patrice Ossona De Mendez

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…

Algebraic Geometry · Mathematics 2020-06-09 Alain Couvreur , Philippe Lebacque , Marc Perret

We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-03 Alkida Balliu , Thomas Boudier , Sebastian Brandt , Dennis Olivetti

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…

Discrete Mathematics · Computer Science 2024-01-04 Miguel Romero , Marcin Wrochna , Stanislav Živný

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…

Optimization and Control · Mathematics 2024-03-15 Frank E. Curtis , Vyacheslav Kungurtsev , Daniel P. Robinson , Qi Wang

There has been a lot of interest recently in proving lower bounds on the size of linear programs needed to represent a given polytope P. In a breakthrough paper Fiorini et al. [Proceedings of 44th ACM Symposium on Theory of Computing 2012,…

Optimization and Control · Mathematics 2013-11-12 Hamza Fawzi , Pablo A. Parrilo

This paper reveals that a common and central role, played in many error bound (EB) conditions and a variety of gradient-type methods, is a residual measure operator. On one hand, by linking this operator with other optimality measures, we…

Optimization and Control · Mathematics 2018-05-17 Hui Zhang

The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an…

Optimization and Control · Mathematics 2015-12-16 Ruoyu Sun , Mingyi Hong

Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…

Discrete Mathematics · Computer Science 2022-07-06 Longkang Li , Baoyuan Wu

We consider a classical scheduling problem on $m$ identical machines. For an arbitrary constant $q>1$, the aim is to assign jobs to machines such that $\sum_{i=1}^m C_i^q$ is minimized, where $C_i$ is the total processing time of jobs…

Computational Complexity · Computer Science 2021-07-14 Lin Chen , Liangde Tao , José Verschae

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…

Symbolic Computation · Computer Science 2025-05-05 Louis Gaillard

Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…

Data Structures and Algorithms · Computer Science 2020-03-03 Grace Dinh , James Demmel

Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…

Computational Complexity · Computer Science 2025-03-18 Florent Foucaud , Esther Galby , Liana Khazaliya , Shaohua Li , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale

We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization.…

Optimization and Control · Mathematics 2020-08-28 Peter Bürgisser , Yinan Li , Harold Nieuwboer , Michael Walter

Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite…

Optimization and Control · Mathematics 2021-08-25 Boro Sofranac , Ambros Gleixner , Sebastian Pokutta