Related papers: A Multi-level Blocking Distinct Degree Factorizati…
We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the…
In sparse LU factorization, nonzero elements after symbolic factorization tend to distribute in diagonal and right-bottom region of sparse matrices. However, regular 2D blocking on this non-uniform distribution structure may lead to…
Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that…
This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and…
We present a new algorithm for the computation of the irreducible factors of degree at most $d$, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero. The algorithm reduces this computation to the…
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…
We propose a multi-stage learning approach for pruning the search space of maximum clique enumeration, a fundamental computationally difficult problem arising in various network analysis tasks. In each stage, our approach learns the…
We study the complexity of polynomial multiplication over arbitrary fields. We present a unified approach that generalizes all known asymptotically fastest algorithms for this problem. In particular, the well-known algorithm for…
We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from the multi-grid community. Local improvement algorithms are based max-flow min-cut computations and…
Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
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…
Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…