Related papers: Chain complex reduction via fast digraph traversal
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
A graph algorithm is truly subquadratic if it runs in ${\cal O}(m^b)$ time on connected $m$-edge graphs, for some positive $b < 2$. Roditty and Vassilevska Williams (STOC'13) proved that under plausible complexity assumptions, there is no…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spaltenstein solved this problem for chain complexes of R-modules by truncating further and further to the left, resolving…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
While programmers know that the low-level memory representation of data structures can have significant effects on performance, compiler support to optimize the layout of those structures is an under-explored field. Prior work has optimized…
Automating design minimizes errors, accelerates the design process, and reduces cost. However, automating robot design is challenging due to recursive constraints, multiple design objectives, and cross-domain design complexity possibly…
We present cuRAMSES, a suite of advanced domain decomposition strategies and algorithmic optimizations for the ramses adaptive mesh refinement (AMR) code, designed to overcome the communication, memory, and solver bottlenecks inherent in…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
We revisit the classical problem of computing the \emph{contour tree} of a scalar field $f:\mathbb{M} \to \mathbb{R}$, where $\mathbb{M}$ is a triangulated simplicial mesh in $\mathbb{R}^d$. The contour tree is a fundamental topological…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…