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There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
In the real world a graph is often fragmented and distributed across different sites. This highlights the need for evaluating queries on distributed graphs. This paper proposes distributed evaluation algorithms for three classes of queries:…
Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…
Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential…
Many computational chemistry and molecular simulation workflows can be expressed as graphs. This abstraction is useful to modularize and potentially reuse existing components, as well as provide parallelization and ease reproducibility.…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
Fast algorithms for optimal multi-robot path planning are sought after in real-world applications. Known methods, however, generally do not simultaneously guarantee good solution optimality and good (e.g., polynomial) running time. In this…
Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network)…
We present an efficient distributed memory parallel algorithm for computing connected components in undirected graphs based on Shiloach-Vishkin's PRAM approach. We discuss multiple optimization techniques that reduce communication volume as…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
Training neural network often uses a machine learning framework such as TensorFlow and Caffe2. These frameworks employ a dataflow model where the NN training is modeled as a directed graph composed of a set of nodes. Operations in neural…
A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple…
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose…
In this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Algebraic data structures are the main subroutine for maintaining distances in fully dynamic graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot maintain the shortest paths, especially against adaptive…
Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…
In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…