14 citations · 47 across the 9 of their papers we have counts for
10 papers
Scalable Algorithms for Approximate DNF Model Counting
Paul Burkhardt, David G. Harris, Kevin T Schmitt
Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability. For example, it is often use…
Simple and efficient four-cycle counting on sparse graphs
Paul Burkhardt, David G. Harris
We consider the problem of counting 4-cycles () in an undirected graph of vertices and edges (in bipartite graphs, 4-cycles are also often referred to as $\textit{…
Triangle Centrality
Paul Burkhardt
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing…
A Simple and Efficient Algorithm for Finding Minimum Spanning Tree Replacement Edges
David A. Bader, Paul Burkhardt
Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applic…
Optimal algebraic Breadth-First Search for sparse graphs
Paul Burkhardt
There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. An exemplar for th…
Graph connectivity in log steps using label propagation
Paul Burkhardt
The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a Parallel Random Access Machine (PRAM). These algorithms mainta…
Bounds and algorithms for graph trusses
Paul Burkhardt, Vance Faber, David G. Harris
The -truss, introduced by Cohen (2005), is a graph where every edge is incident to at least triangles. This is a relaxation of the clique. It has proved to be a useful tool…
Random Matrix Ensembles with Split Limiting Behavior
Paula Burkhardt, Peter Cohen, Jonathan Dewitt +6
We introduce a new family of random real symmetric matrix ensembles, the -checkerboard matrices, whose limiting spectral measure has two components which can be dete…
One-Level density for holomorphic cusp forms of arbitrary level
Owen Barrett, Paula Burkhardt, Jonathan DeWitt +2
In 2000 Iwaniec, Luo, and Sarnak proved for certain families of -functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis…
Visual properties of generalized Kloosterman sums
Paula Burkhardt, Alice Zhuo-Yu Chan, Gabriel Currier +3
For a positive integer and a subgroup of the unit group , the corresponding generalized Kloosterman sum is the function $K(a,b,m,Λ) = \sum_…