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We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy.…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem). We have developed an efficient algorithm for light spanners in bounded pathwidth graphs, based…
Given a 2-edge connected, unweighted, and undirected graph $G$ with $n$ vertices and $m$ edges, a $\sigma$-tree spanner is a spanning tree $T$ of $G$ in which the ratio between the distance in $T$ of any pair of vertices and the…
It is $\mathsf{NP}$-hard to determine the minimum number of branching vertices needed in a single-source distance-preserving subgraph of an undirected graph. We show that this problem can be solved in polynomial time if the input graph is…
A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of $G$ to a sequence of horizontal…
Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…
Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point.…
Tree spanners approximate distances within graphs; a subtree of a graph is a tree $t$-spanner of the graph if and only if for every pair of vertices their distance in the subtree is at most $t$ times their distance in the graph. When a…
In this report we discuss the concepts of geometric memory align- ment, geometric memory allocation and geometric memory mapping. We introduce block trees as an efficient data structure for representing geo- metrically aligned block…
Multimodal machine learning has been widely studied for the development of general intelligence. Recently, the Perceiver and Perceiver IO, show competitive results for diverse dataset domains and tasks. However, recent works, Perceiver and…
Distributed algorithms are often beset by the straggler effect, where the slowest compute nodes in the system dictate the overall running time. Coding-theoretic techniques have been recently proposed to mitigate stragglers via algorithmic…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Hierarchical clustering over graphs is a fundamental task in data mining and machine learning with applications in domains such as phylogenetics, social network analysis, and information retrieval. Specifically, we consider the recently…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures…
A $t$-{\em spanner} $H$ of a weighted graph $G=(V,E,w)$ is a subgraph that approximates all pairwise distances up to a factor of $t$. The {\em lightness} of $H$ is defined as the ratio between the weight of $H$ to that of the minimum…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…