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This paper shows how to generate efficient tensor algebra code that compute on dynamic sparse tensors, which have sparsity structures that evolve over time. We propose a language for precisely specifying recursive, pointer-based data…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for solving system of linear equations, form the kernel…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems.…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We…
Sparse computations frequently appear in scientific simulations and the performance of these simulations rely heavily on the optimization of the sparse codes. The compact data structures and irregular computation patterns in sparse matrix…
We are interested in unsupervised reconstruction of complex near-capillary vasculature with thousands of bifurcations where supervision and learning are infeasible. Unsupervised methods can use many structural constraints, e.g. topology,…
To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still…
We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
Robin Forman's highly influential 2002 paper A User's Guide to Discrete Morse Theory presents an overview of the subject in a very readable manner. As a proof of concept, the author determines the topology (homotopy type) of the abstract…
Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD). Previously, there has been…
We introduce novel methods for encoding acyclicity and s-t-reachability constraints for propositional formulas with underlying directed graphs. They are based on vertex elimination graphs, which makes them suitable for cases where the…