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Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths…
The Graph Convolutional Network (GCN) model and its variants are powerful graph embedding tools for facilitating classification and clustering on graphs. However, a major challenge is to reduce the complexity of layered GCNs and make them…
To effectively control large-scale distributed systems online, model predictive control (MPC) has to swiftly solve the underlying high-dimensional optimization. There are multiple techniques applied to accelerate the solving process in the…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
Optical flow estimation is crucial for autonomous navigation and localization of unmanned aerial vehicles (UAV). On micro and nano UAVs, real-time calculation of the optical flow is run on low power and resource-constrained microcontroller…
Leveraging Trace Theory, we investigate the efficient parallelization of direct solvers for large linear equation systems. Our focus lies on a multi-frontal algorithm, and we present a methodology for achieving near-optimal scheduling on…
We consider the problem of designing deterministic graph algorithms for the model of Massively Parallel Computation (MPC) that improve with the sparsity of the input graph, as measured by the notion of arboricity. For the problems of…
This paper describes the parallel implementation of the TRANSIMS traffic micro-simulation. The parallelization method is domain decomposition, which means that each CPU of the parallel computer is responsible for a different geographical…
This paper discusses opportunities to parallelize graph based path planning algorithms in a time varying environment. Parallel architectures have become commonplace, requiring algorithm to be parallelized for efficient execution. An…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
We present an $\tilde O(m+n^{1.5})$-time randomized algorithm for maximum cardinality bipartite matching and related problems (e.g. transshipment, negative-weight shortest paths, and optimal transport) on $m$-edge, $n$-node graphs. For…
Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time…
With the rapid growth of unstructured and semistructured data, parallelizing graph algorithms has become essential for efficiency. However, due to the inherent irregularity in computation, memory access patterns, and communication, graph…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
In this paper, we study the problem of maximizing a monotone normalized one-sided $\sigma$-smooth ($OSS$ for short) function $F(x)$, subject to a convex polytope. This problem was first introduced by Mehrdad et al. \cite{GSS2021} to…
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…
A minimum path cover (MPC) of a directed acyclic graph (DAG) $G = (V,E)$ is a minimum-size set of paths that together cover all the vertices of the DAG. Computing an MPC is a basic polynomial problem, dating back to Dilworth's and…