相关论文: Efficient cache use for stencil operations on stru…
Recent studies highlighting the vulnerability of computer architecture to information leakage attacks have been a cause of significant concern. Among the various classes of microarchitectural attacks, cache timing channels are especially…
An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let $Ext_{\alpha}$ be the class of all connected graphs whose quotient graph obtained from modular…
Spatial computing devices have been shown to significantly accelerate stencil computations, but have so far relied on unrolling the iterative dimension of a single stencil operation to increase temporal locality. This work considers the…
In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…
Caching is crucial for system performance, but the delayed hit phenomenon, where requests queue during lengthy fetches after a cache miss, significantly degrades user-perceived latency in modern high-throughput systems. While prior works…
We provide a doubly exponential upper bound in $p$ on the size of forbidden pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field $\mathbb{F}$ of linear rank-width at most $p$. As a corollary, we obtain a doubly…
We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. All of our algorithms run in O(n) time, where n is the number of vertices in the graph. In our proofs, we present an embedding algorithm for…
In recommendation systems, practitioners observed that increase in the number of embedding tables and their sizes often leads to significant improvement in model performances. Given this and the business importance of these models to major…
This paper studies the lattice agreement problem and proposes a stronger form, $\varepsilon$-bounded lattice agreement, that enforces an additional tightness constraint on the outputs. To formalize the concept, we define a quasi-metric on…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
This paper presents a distributed algorithm for finding near optimal dominating sets on grids. The basis for this algorithm is an existing centralized algorithm that constructs dominating sets on grids. The size of the dominating set…
We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the…
A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ…
As the discretization error for the solution of a partial differential equation (PDE) decreases, the precision required to store the corresponding coefficients naturally increases. Storing the solution's finite element coefficients…
An efficient method is described to handle mesh indexes in multidimensional problems like numerical integration of partial differential equations, lattice model simulations, and determination of atomic neighbor lists. By creating an…
Deep networks are nowadays becoming popular in many computer vision and pattern recognition tasks. Among these networks, deep kernels are particularly interesting and effective, however, their computational complexity is a major issue…
We give structured proofs for five mathematical propositions governing synchronous peer-to-peer computation on a finite grid graph embedded in $\mathbb{Z}^2$. Proposition 1 gives three lower bounds: a transport-work bound $\sum_i a_i \ell_i…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
Hypergraph partitioning is a pervasive NP-hard problem, and accelerating its computation on GPU can both slice time-to-solution and raise quality of results. In this work, we implement a multi-level hypergraph partitioning algorithm on GPU…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…