Structures from Distances in Two and Three Dimensions using Stochastic Proximity Embedding

The point placement problem is to determine the locations of a set of distinct points uniquely (up to translation and reflection) by making the fewest possible pairwise distance queries of an adversary. Deterministic and randomized algorithms are available if distances are known exactly. In this thesis, we discuss a 1-round algorithm for approximate point placement in the plane in an adversarial model. The distance query graph presented to the adversary is chordal. The remaining distances are uniquely determined using the Stochastic Proximity Embedding (SPE) method due to Agrafiotis, and the layout of the points is also generated from SPE. We have also computed the distances uniquely using a distance matrix completion algorithm for chordal graphs, based on a result by Bakonyi and Johnson. The layout of the points is determined using the traditional Young- Householder approach. We compared the layout of both the method and discussed briefly inside. The modified version of SPE is proposed to overcome the highest translation embedding that the method faces when dealing with higher learning rates. We also discuss the computation of molecular structures in three-dimensional space, with only a subset of the pairwise atomic distances available. The subset of distances is obtained using the Philips model for creating artificial backbone chain of molecular structures. We have proposed the Degree of Freedom Approach to solve this problem and carried out our implementation using SPE and the Distance matrix completion Approac

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms

Chordal Graphs and Their Relatives: Algorithms and Applications

While the problem of generating random graphs has received much attention, the problem of generating graphs for specific classes has not been studied much. In this dissertation, we propose schemes for generating chordal graphs, weakly chordal graphs, and strongly chordal graphs. We also present semi-dynamic algorithms for chordal graphs and strongly chordal graphs. As an application of a completion technique for chordal graphs, we also discuss a 1-round algorithm for approximate point placement in the plane in an adversarial model where the distance query graph presented to the adversary is chordal. The proposed generation algorithms take the number of vertices, n, and the number of edges, m, as input and produces a graph in a given class as output. The generation method either starts with a tree or a complete graph. We then insert additional edges in the tree or delete edges from the complete graph. Our algorithm ensures that the graph properties are preserved after each edge is inserted or deleted. We have also proposed algorithms to generate weakly chordal graphs and strongly chordal graphs from an arbitrary graph as input. In this case, we ensure the graph properties will be achieved on the termination of the conversion process. We have also proposed a semi-dynamic algorithm for edge-deletion in a chordal graph. To the best of our knowledge, no study has been done for the problem of dynamic algorithms for strongly chordal graphs. To address this gap, we have also proposed a semi-dynamic algorithm for edge-deletions and a semi-dynamic algorithm for edge-insertions in strongly chordal graphs

Conserve and Protect Resources in Software-Defined Networking via the Traffic Engineering Approach

Software Defined Networking (SDN) is revolutionizing the architecture and operation of computer networks and promises a more agile and cost-efficient network management. SDN centralizes the network control logic and separates the control plane from the data plane, thus enabling flexible management of networks. A network based on SDN consists of a data plane and a control plane. To assist management of devices and data flows, a network also has an independent monitoring plane. These coexisting network planes have various types of resources, such as bandwidth utilized to transmit monitoring data, energy spent to power data forwarding devices and computational resources to control a network. Unwise management, even abusive utilization of these resources lead to the degradation of the network performance and increase the Operating Expenditure (Opex) of the network owner. Conserving and protecting limited network resources is thus among the key requirements for efficient networking. However, the heterogeneity of the network hardware and network traffic workloads expands the configuration space of SDN, making it a challenging task to operate a network efficiently. Furthermore, the existing approaches usually lack the capability to automatically adapt network configurations to handle network dynamics and diverse optimization requirements. Addtionally, a centralized SDN controller has to run in a protected environment against certain attacks. This thesis builds upon the centralized management capability of SDN, and uses cross-layer network optimizations to perform joint traffic engineering, e.g., routing, hardware and software configurations. The overall goal is to overcome the management complexities in conserving and protecting resources in multiple functional planes in SDN when facing network heterogeneities and system dynamics. This thesis presents four contributions: (1) resource-efficient network monitoring, (2) resource-efficient data forwarding, (3) using self-adaptive algorithms to improve network resource efficiency, and (4) mitigating abusive usage of resources for network controlling. The first contribution of this thesis is a resource-efficient network monitoring solution. In this thesis, we consider one specific type of virtual network management function: flow packet inspection. This type of the network monitoring application requires to duplicate packets of target flows and send them to packet monitors for in-depth analysis. To avoid the competition for resources between the original data and duplicated data, the network operators can transmit the data flows through physically (e.g., different communication mediums) or virtually (e.g., distinguished network slices) separated channels having different resource consumption properties. We propose the REMO solution, namely Resource Efficient distributed Monitoring, to reduce the overall network resource consumption incurred by both types of data, via jointly considering the locations of the packet monitors, the selection of devices forking the data packets, and flow path scheduling strategies. In the second contribution of this thesis, we investigate the resource efficiency problem in hybrid, server-centric data center networks equipped with both traditional wired connections (e.g., InfiniBand or Ethernet) and advanced high-data-rate wireless links (e.g., directional 60GHz wireless technology). The configuration space of hybrid SDN equipped with both wired and wireless communication technologies is massively large due to the complexity brought by the device heterogeneity. To tackle this problem, we present the ECAS framework to reduce the power consumption and maintain the network performance. The approaches based on the optimization models and heuristic algorithms are considered as the traditional way to reduce the operation and facility resource consumption in SDN. These approaches are either difficult to directly solve or specific for a particular problem space. As the third contribution of this thesis, we investigates the approach of using Deep Reinforcement Learning (DRL) to improve the adaptivity of the management modules for network resource and data flow scheduling. The goal of the DRL agent in the SDN network is to reduce the power consumption of SDN networks without severely degrading the network performance. The fourth contribution of this thesis is a protection mechanism based upon flow rate limiting to mitigate abusive usage of the SDN control plane resource. Due to the centralized architecture of SDN and its handling mechanism for new data flows, the network controller can be the failure point due to the crafted cyber-attacks, especially the Control-Plane- Saturation (CPS) attack. We proposes an In-Network Flow mAnagement Scheme (INFAS) to effectively reduce the generation of malicious control packets depending on the parameters configured for the proposed mitigation algorithm. In summary, the contributions of this thesis address various unique challenges to construct resource-efficient and secure SDN. This is achieved by designing and implementing novel and intelligent models and algorithms to configure networks and perform network traffic engineering, in the protected centralized network controller

Multi-Robot Task Allocation: A Spatial Queuing Approach

Multi-Robot Task Allocation (MRTA) is an important area of research in autonomous multi-robot systems. The main problem in MRTA is to match a set of robots to a set of tasks so that the tasks can be completed by the robots while optimizing a certain metric such as the time required to complete all tasks, distance traveled by the robots and energy expended by the robots. We consider a scenario where the tasks can appear dynamically and the location of tasks are not known a priori by the robots. Additionally, for a task to be completed, it needs to be performed by multiple robots. This setting is called the MR-ST-TA (multi-robot, single-task, time- extended assginment) category of MRTA; solving the MRTA problem for this category is a known NP-hard problem. In this thesis, we address this problem by proposing a new algorithm that uses a spatial queue-based model to allocate tasks between robots while comparing its performance to several other known methods. We have implemented these algorithms on an accurately simulated model of Corobot robots within the Webots simulator for different numbers of robots and tasks. The results show that our method is adept in all proffered environments, especially scenarios that benefit from path planning, whereas other methods display inherent weakness at one end of the spectrum: a decentralized greedy approach exhibits inefficient behavior as the robot to task ratio dips below one, whereas the Hungarian method (an offline algorithm) fails to keep pace as the robot count increases

Tetrahedral Meshes in Biomedical Applications: Generation, Boundary Recovery and Quality Enhancements

Mesh generation is a fundamental precursor to finite element implementations for solution of partial differential equations in engineering and science. This dissertation advances the field in three distinct but coupled areas. A robust and fast three dimensional mesh generator for arbitrarily shaped geometries was developed. It deploys nodes throughout the domain based upon user-specified mesh density requirements. The system is integer and pixel based which eliminates round off errors, substantial memory requirements and cpu intensive calculations. Linked, but fully detachable, to the mesh generation system is a physical boundary recovery routine. Frequently, the original boundary topology is required for specific boundary condition applications or multiple material constraints. Historically, this boundary preservation was not available. An algorithm was developed, refined and optimized that recovers the original boundaries, internal and external, with fidelity. Finally, a node repositioning algorithm was developed that maximizes the minimum solid angle of tetrahedral meshes. The highly coveted 2D Delaunay property that maximizes the minimum interior angle of a triangle mesh does not extend to its 3D counterpart, to maximize the minimum solid angle of a tetrahedron mesh. As a consequence, 3D Delaunay created meshes have unacceptable sliver tetrahedral elements albeit composed of 4 high quality triangle sides. These compromised elements are virtually unavoidable and can foil an otherwise intact mesh. The numerical optimization routine developed takes any preexisting tetrahedral mesh and repositions the nodes without changing the mesh topology so that the minimum solid angle of the tetrahedrons is maximized. The overall quality enhancement of the volume mesh might be small, depending upon the initial mesh. However, highly distorted elements that create ill-conditioned global matrices and foil a finite element solver are enhanced significantly

Online Planning for Autonomous Running Jumps Over Obstacles in High-Speed Quadrupeds

This paper presents a new framework for the generation of high-speed running jumps to clear terrain obstacles in quadrupedal robots. Our methods enable the quadruped to autonomously jump over obstacles up to 40 cm in height within a single control framework. Specifically, we propose new control system components, layered on top of a low-level running controller, which actively modify the approach and select stance force profiles as required to clear a sensed obstacle. The approach controller enables the quadruped to end in a preferable state relative to the obstacle just before the jump. This multi-step gait planning is formulated as a multiple-horizon model predictive control problem and solved at each step through quadratic programming. Ground reaction force profiles to execute the running jump are selected through constrained nonlinear optimization on a simplified model of the robot that possesses polynomial dynamics. Exploiting the simplified structure of these dynamics, the presented method greatly accelerates the computation of otherwise costly function and constraint evaluations that are required during optimization. With these considerations, the new algorithms allow for online planning that is critical for reliable response to unexpected situations. Experimental results, for a stand-alone quadruped with on-board power and computation, show the viability of this approach, and represent important steps towards broader dynamic maneuverability in experimental machines.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) ProgramKorean Agency for Defense Development (Contract UD1400731D