相关论文: I/O Efficient Algorithms for Matrix Computations
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times…
Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…
We introduce the fastest known exact algorithm~for~the multiterminal cut problem with k terminals. In particular, we engineer existing as well as new data reduction rules. We use the rules within a branch-and-reduce framework and to boost…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Sublinear time quantum algorithms have been established for many fundamental problems on strings. This work demonstrates that new, faster quantum algorithms can be designed when the string is highly compressible. We focus on two popular and…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
This paper addresses the problem of optimizing communicated information among heterogeneous, resource-aware robot teams to facilitate their navigation. In such operations, a mobile robot compresses its local map to assist another robot in…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
Dearing and Zeck presented a dual algorithm for the problem of the minimum covering ball in $\mathbb{R}^n$. Each iteration of their algorithm has a computational complexity of at least $\mathcal O(n^3)$. In this paper we propose a…
Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations,…
In this work, we provide the first QFT-free algorithm for Quantum Amplitude Estimation (QAE) that is asymptotically optimal while maintaining the leading numerical performance. QAE algorithms appear as a subroutine in many applications for…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
A two-user downlink network aided by a reconfigurable intelligent surface is considered. The weighted sum signal to interference plus noise ratio maximization and the sum rate maximization models are presented, where the precoding vectors…