Related papers: Persistent (Co)Homology in Matrix Multiplication T…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
We construct worst-case examples for the standard reduction algorithm for computing persistent homology. Our constructions are similar to the worst-case examples introduced by Morozov, but we replace the single-triangle arrangement with a…
Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing…
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the…
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
We describe an algorithm to compute the stable multiplicity of a family of irreducible representations in the cohomology of ordered configuration space of the plane. Using this algorithm, we compute the stable multiplicities of all families…