相关论文: A Non-iterative Parallelizable Eigenbasis Algorith…

We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…

We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…

We present a new approach to the minimum-cost integral flow problem for small values of the flow. It reduces the problem to the tests of simple multi-variate polynomials over a finite field of characteristic two for non-identity with zero.…

Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…

We consider the classical $k$-Center problem in undirected graphs. The problem is known to have a polynomial-time 2-approximation. There are even $(2+\varepsilon)$-approximations running in near-linear time. The conventional wisdom is that…

We give a $O^*(k^{O(k)})$ time isomorphism testing algorithm for graphs of eigenvalue multiplicity bounded by $k$ which improves on the previous best running time bound of $O^*(2^{O(k^2/\log k)})$.

We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…

The set $X$ of $k$-subsets of an $n$-set has a natural graph structure where two $k$-subsets are connected if and only if the size of their intersection is $k-1$. This is known as the Johnson graph. The symmetric group $S_n$ acts on the…

We propose an efficient algorithm for matching two correlated Erd\H{o}s--R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence. When the edge density $q= n^{- \alpha+o(1)}$ for a constant $\alpha…

We study a $(1+\epsilon)$-approximate single-source shortest paths (henceforth, $(1+\epsilon)$-SSSP) in $n$-vertex undirected, weighted graphs in the parallel (PRAM) model of computation. A randomized algorithm with polylogarithmic time and…

In this paper, we study the \textsf{Planar Disjoint Paths} problem: Given an undirected planar graph $G$ with $n$ vertices and a set $T$ of $k$ pairs $(s_i,t_i)_{i=1}^k$ of vertices, the goal is to find a set $\mathcal P$ of $k$ pairwise…

We present an algorithm that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in $\tilde{O}(n^{4/3}m^{1/2}+n^{2})$ time (The $\tilde{O}(\cdot)$ notation hides $\operatorname{polylog}(n)$…

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…

We analyze several versions of Jacobi's method for the symmetric eigenvalue problem. Our goal is to reduce the asymptotic cost of the algorithm as much as possible, as measured by the number of arithmetic operations performed and associated…

We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of…

We present an algorithm which can generate all pairwise non-isomorphic $K_2$-hypohamiltonian graphs, i.e. non-hamiltonian graphs in which the removal of any pair of adjacent vertices yields a hamiltonian graph, of a given order. We…

We have developed a parallel algorithm for radial basis function (RBF) interpolation that exhibits O(N) complexity,requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a GMRES iterative solver with a…

In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…