Guarding and Searching Polyhedra

Guarding and searching problems have been of fundamental interest since the early years of Computational Geometry. Both are well-developed areas of research and have been thoroughly studied in planar polygonal settings. In this thesis we tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra. We solve the Art Gallery Problem with reflex edge guards in orthogonal polyhedra having reflex edges in just two directions: generalizing a classic theorem by O'Rourke, we prove that r/2 + 1 reflex edge guards are sufficient and occasionally necessary, where r is the number of reflex edges. We also show how to compute guard locations in O(n log n) time. Then we investigate the Art Gallery Problem with mutually parallel edge guards in orthogonal polyhedra with e edges, showing that 11e/72 edge guards are always sufficient and can be found in linear time, improving upon the previous state of the art, which was e/6. We also give tight inequalities relating e with the number of reflex edges r, obtaining an upper bound on the guard number of 7r/12 + 1. We further study the Art Gallery Problem with edge guards in polyhedra having faces oriented in just four directions, obtaining a lower bound of e/6 - 1 edge guards and an upper bound of (e+r)/6 edge guards. All the previously mentioned results hold for polyhedra of any genus. Additionally, several guard types and guarding modes are discussed, namely open and closed edge guards, and orthogonal and non-orthogonal guarding. Next, we model the Searchlight Scheduling Problem, the problem of searching a given polyhedron by suitably turning some half-planes around their axes, in order to catch an evasive intruder. After discussing several generalizations of classic theorems, we study the problem of efficiently placing guards in a given polyhedron, in order to make it searchable. For general polyhedra, we give an upper bound of r^2 on the number of guards, which reduces to r for orthogonal polyhedra. Then we prove that it is strongly NP-hard to decide if a given polyhedron is entirely searchable by a given set of guards. We further prove that, even under the assumption that an orthogonal polyhedron is searchable, approximating the minimum search time within a small-enough constant factor to the optimum is still strongly NP-hard. Finally, we show that deciding if a specific region of an orthogonal polyhedron is searchable is strongly PSPACE-hard. By further improving our construction, we show that the same problem is strongly PSPACE-complete even for planar orthogonal polygons. Our last results are especially meaningful because no similar hardness theorems for 2-dimensional scenarios were previously known

Connectivity Constraints in Network Analysis

This dissertation establishes mathematical foundations of connectivity requirements arising in both abstract and geometric network analysis. Connectivity constraints are ubiquitous in network design and network analysis. Aside from the obvious applications in communication and transportation networks, they have also appeared in forest planning, political distracting, activity detection in video sequences and protein-protein interaction networks. Theoretically, connectivity constraints can be analyzed via polyhedral methods, in which we investigate the structure of (vertex)-connected subgraph polytope (CSP). One focus of this dissertation is on performing an extensive study of facets of CSP. We present the first systematic study of non-trivial facets of CSP. One advantage to study facets is that a facet-defining inequality is always among the tightest valid inequalities, so applying facet-defining inequalities when imposing connectivity constraints can guarantee good performance of the algorithm. We adopt lifting techniques to provide a framework to generate a wide class of facet-defining inequalities of CSP. We also derive the necessary and sufficient conditions when a vertex separator inequality, which plays a critical role in connectivity constraints, induces a facet of CSP. Another advantage to study facets is that CSP is uniquely determined by its facets, so full understanding of CSP's facets indicates full understanding of CSP itself. We are able to derive a full description of CSP for a wide class of graphs, including forest and several types of dense graphs, such as graphs with small independence number, s-plex with small s and s-defective cliques with small s. Furthermore, we investigate the relationship between lifting techniques, maximum weight connected subgraph problem and node-weight Steiner tree problem and study the computational complexity of generation of facet-defining inequalities. Another focus of this dissertation is to study connectivity in geometric network analysis. In geometric applications like wireless networks and communication networks, the concept of connectivity can be defined in various ways. In one case, connectivity is imposed by distance, which can be modeled by unit disk graphs (UDG). We create a polytime algorithm to identify large 2-clique in UDG; in another case when connectivity is based on visibility, we provide a generalization of the two-guard problem

Ranked Similarity Search of Scientific Datasets: An Information Retrieval Approach

In the past decade, the amount of scientific data collected and generated by scientists has grown dramatically. This growth has intensified an existing problem: in large archives consisting of datasets stored in many files, formats and locations, how can scientists find data relevant to their research interests? We approach this problem in a new way: by adapting Information Retrieval techniques, developed for searching text documents, into the world of (primarily numeric) scientific data. We propose an approach that uses a blend of automated and curated methods to extract metadata from large repositories of scientific data. We then perform searches over this metadata, returning results ranked by similarity to the search criteria. We present a model of this approach, and describe a specific implementation thereof performed at an ocean-observatory data archive and now running in production. Our prototype implements scanners that extract metadata from datasets that contain different kinds of environmental observations, and a search engine with a candidate similarity measure for comparing a set of search terms to the extracted metadata. We evaluate the utility of the prototype by performing two user studies; these studies show that the approach resonates with users, and that our proposed similarity measure performs well when analyzed using standard Information Retrieval evaluation methods. We performed performance tests to explore how continued archive growth will affect our goal of interactive response, developed and applied techniques that mitigate the effects of that growth, and show that the techniques are effective. Lastly, we describe some of the research needed to extend this initial work into a true Google for data

High-throughput visual knowledge analysis and retrieval in big data ecosystems

Visual knowledge plays an important role in many highly skilled applications, such as medical diagnosis, geospatial image analysis and pathology diagnosis. Medical practitioners are able to interpret and reason about diagnostic images based on not only primitive-level image features such as color, texture, and spatial distribution but also their experience and tacit knowledge which are seldom articulated explicitly. This reasoning process is dynamic and closely related to real-time human cognition. Due to a lack of visual knowledge management and sharing tools, it is difficult to capture and transfer such tacit and hard-won expertise to novices. Moreover, many mission-critical applications require the ability to process such tacit visual knowledge in real time. Precisely how to index this visual knowledge computationally and systematically still poses a challenge to the computing community. My dissertation research results in novel computational approaches for high-throughput visual knowledge analysis and retrieval from large-scale databases using latest technologies in big data ecosystems. To provide a better understanding of visual reasoning, human gaze patterns are qualitatively measured spatially and temporally to model observers' cognitive process. These gaze patterns are then indexed in a NoSQL distributed database as a visual knowledge repository, which is accessed using various unique retrieval methods developed through this dissertation work. To provide meaningful retrievals in real time, deep-learning methods for automatic annotation of visual activities and streaming similarity comparisons are developed under a gaze-streaming framework using Apache Spark. This research has several potential applications that offer a broader impact among the scientific community and in the practical world. First, the proposed framework can be adapted for different domains, such as fine arts, life sciences, etc. with minimal effort to capture human reasoning processes. Second, with its real-time visual knowledge search function, this framework can be used for training novices in the interpretation of domain images, by helping them learn experts' reasoning processes. Third, by helping researchers to understand human visual reasoning, it may shed light on human semantics modeling. Finally, integrating reasoning process with multimedia data, future retrieval of media could embed human perceptual reasoning for database search beyond traditional content-based media retrievals

Journal of Telecommunications and Information Technology, 2014, nr 4

kwartalni

Volume 20 - 1989: FRONTIERS IN GEOSCIENCE INFORMATION - Proceedings of the 24th Meeting of the Geoscience Information Society

Proceedings of the 24th Meeting of the Geoscience Information Society held November 6-9, 1989 in St. Louis, Missour

NASA Tech Briefs, August 1993

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