Related papers: A new transfer-matrix algorithm for exact enumerat…
We study the problem of estimating the trace of a matrix $A$ that can only be accessed through matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which computes a $(1 \pm \epsilon)$ approximation to $tr(A)$ for…
The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries.…
Many lattice-based crypstosystems employ ideal lattices for high efficiency. However, the additional algebraic structure of ideal lattices usually makes us worry about the security, and it is widely believed that the algebraic structure…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
Let $G$ be an infinite, vertex-transitive lattice with degree $\lambda$ and fix a vertex on it. Consider all cycles of length exactly $l$ from this vertex to itself on $G$. Erasing loops chronologically from these cycles, what is the…
Structured data, which constitutes a significant portion of existing data types, has been a long-standing research topic in the field of machine learning. Various representation learning methods for tabular data have been proposed, ranging…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
Minimax distance measure extracts the underlying patterns and manifolds in an unsupervised manner. The existing methods require a quadratic memory with respect to the number of objects. In this paper, we investigate efficient sampling…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The…
The question of list decoding error-correcting codes over finite fields (under the Hamming metric) has been widely studied in recent years. Motivated by the similar discrete structure of linear codes and point lattices in R^N, and their…
We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask…
In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
The model of self-avoiding lattice walks and the asymptotic analysis of power-series have been two of the major research themes of Tony Guttmann. In this paper we bring the two together and perform a new analysis of the generating functions…