Real-time analytics on large dynamic graphs

In today's fast-paced and interconnected digital world, the data generated by an increasing number of applications is being modeled as dynamic graphs. The graph structure encodes relationships among data items, while the structural changes to the graphs as well as the continuous stream of information produced by the entities in these graphs make them dynamic in nature. Examples include social networks where users post status updates, images, videos, etc.; phone call networks where nodes may send text messages or place phone calls; road traffic networks where the traffic behavior of the road segments changes constantly, and so on. There is a tremendous value in storing, managing, and analyzing such dynamic graphs and deriving meaningful insights in real-time. However, a majority of the work in graph analytics assumes a static setting, and there is a lack of systematic study of the various dynamic scenarios, the complexity they impose on the analysis tasks, and the challenges in building efficient systems that can support such tasks at a large scale. In this dissertation, I design a unified streaming graph data management framework, and develop prototype systems to support increasingly complex tasks on dynamic graphs. In the first part, I focus on the management and querying of distributed graph data. I develop a hybrid replication policy that monitors the read-write frequencies of the nodes to decide dynamically what data to replicate, and whether to do eager or lazy replication in order to minimize network communication and support low-latency querying. In the second part, I study parallel execution of continuous neighborhood-driven aggregates, where each node aggregates the information generated in its neighborhoods. I build my system around the notion of an aggregation overlay graph, a pre-compiled data structure that enables sharing of partial aggregates across different queries, and also allows partial pre-computation of the aggregates to minimize the query latencies and increase throughput. Finally, I extend the framework to support continuous detection and analysis of activity-based subgraphs, where subgraphs could be specified using both graph structure as well as activity conditions on the nodes. The query specification tasks in my system are expressed using a set of active structural primitives, which allows the query evaluator to use a set of novel optimization techniques, thereby achieving high throughput. Overall, in this dissertation, I define and investigate a set of novel tasks on dynamic graphs, design scalable optimization techniques, build prototype systems, and show the effectiveness of the proposed techniques through extensive evaluation using large-scale real and synthetic datasets.

Automated Software Debugging Using Hybrid Static/Dynamic Analysis

With the increasing complexity of today's software, the software development process is becoming highly time and resource consuming. The increasing number of software configurations, input parameters, usage scenarios, supporting platforms, external dependencies, and versions plays an important role in expanding the costs of maintaining and repairing unforeseeable software faults. To repair software faults, developers spend considerable time in identifying the scenarios leading to those faults and root-causing the problems. While software debugging remains largely manual, it is not the case with software testing and verification. The goal of this research is to improve the software development process in general, and software debugging process in particular, by devising techniques and methods for automated software debugging, which leverage the advances in automatic test case generation and replay. In this research, novel algorithms are devised to discover faulty execution paths in programs by utilizing already existing software test cases, which can be either automatically or manually generated. The execution traces, or alternatively, the sequence covers of the failing test cases are extracted. Afterwards, commonalities between these test case sequence covers are extracted, processed, analyzed, and then presented to the developers in the form of subsequences that may be causing the fault. The hypothesis is that code sequences that are shared between a number of faulty test cases for the same reason resemble the faulty execution path, and hence, the search space for the faulty execution path can be narrowed down by using a large number of test cases. To achieve this goal, an efficient algorithm is implemented for finding common subsequences among a set of code sequence covers. Optimization techniques are devised to generate shorter and more logical sequence covers, and to select subsequences with high likelihood of containing the root cause among the set of all possible common subsequences. A hybrid static/dynamic analysis approach is designed to trace back the common subsequences from the end to the root cause. A debugging tool is created to enable developers to use the approach, and integrate it with an existing Integrated Development Environment. The tool is also integrated with the environment's program editors so that developers can benefit from both the tool suggestions, and their source code counterparts. Finally, a comparison between the developed approach and the state-of-the-art techniques shows that developers need only to inspect a small number of lines in order to find the root cause of the fault. Furthermore, experimental evaluation shows that the algorithm optimizations lead to better results in terms of both the algorithm running time and the output subsequence length.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

RISK-BASED MULTIOBJECTIVE PATH PLANNING AND DESIGN OPTIMIZATION FOR UNMANNED AERIAL VEHICLES

Safe operation of unmanned aerial vehicles (UAVs) over populated areas requires reducing the risk posed by a UAV if it crashed during its operation. We considered several types of UAV risk-based path planning problems and developed techniques for estimating the risk to third parties on the ground. The path planning problem requires making trade-offs between risk and flight time. Four optimization approaches for solving the problem were tested; a network-based approach that used a greedy algorithm to improve the original solution generated the best solutions with the least computational effort. Additionally, an approach for solving a combined design and path planning problems was developed and tested. This approach was extended to solve robust risk-based path planning problem in which uncertainty about wind conditions would affect the risk posed by a UAV.