Algorithms for Optimizing Search Schedules in a Polygon

In the area of motion planning, considerable work has been done on guarding problems, where "guards", modelled as points, must guard a polygonal space from "intruders". Different variants of this problem involve varying a number of factors. The guards performing the search may vary in terms of their number, their mobility, and their range of vision. The model of intruders may or may not allow them to move. The polygon being searched may have a specified starting point, a specified ending point, or neither of these. The typical question asked about one of these problems is whether or not certain polygons can be searched under a particular guarding paradigm defined by the types of guards and intruders. In this thesis, we focus on two cases of a chain of guards searching a room (polygon with a specific starting point) for mobile intruders. The intruders must never be allowed to escape through the door undetected. In the case of the two guard problem, the guards must start at the door point and move in opposite directions along the boundary of the polygon, never crossing the door point. At all times, the guards must be able to see each other. The search is complete once both guards occupy the same spot elsewhere on the polygon. In the case of a chain of three guards, consecutive guards in the chain must always be visible. Again, the search starts at the door point, and the outer guards of the chain must move from the door in opposite directions. These outer guards must always remain on the boundary of the polygon. The search is complete once the chain lies entirely on a portion of the polygon boundary not containing the door point. Determining whether a polygon can be searched is a problem in the area of visibility in polygons; further to that, our work is related to the area of planning algorithms. We look for ways to find optimal schedules that minimize the distance or time required to complete the search. This is done by finding shortest paths in visibility diagrams that indicate valid positions for the guards. In the case of the two-guard room search, we are able to find the shortest distance schedule and the quickest schedule. The shortest distance schedule is found in O(n^2) time by solving an L_1 shortest path problem among curved obstacles in two dimensions. The quickest search schedule is found in O(n^4) time by solving an L_infinity shortest path problem among curved obstacles in two dimensions. For the chain of three guards, a search schedule minimizing the total distance travelled by the outer guards is found in O(n^6) time by solving an L_1 shortest path problem among curved obstacles in two dimensions

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

Appalachia Summer/Fall 2014: Complete Issue

Summer/Fall 2014 - Volume LXV, Number 2 - issue #238. Many Miles: You Can\u27t Run That and Other Chronicle

The Integration of a Coal Mine Emergency Communication Network into Pre-Mine Planning and Development

Regulations, such as the MINER Act of 2006, require the installation of redundant and secondary communication systems to assure that contact can be established with coal miners who may become trapped underground as a result of an event such as a fire, explosion, or inundation. For half a century, the orientation towards underground communications has been that more complex systems better serve the coal miner. However, if the goal is to provide for a reliable means of establishing communication between the surface and trapped miners underground, then the technology employed should be simple, reliable, and cost-effective. Coal mines spend hundreds of thousands of dollars on exploratory drillholes to characterize reserves, sometimes decades ahead of mine development. During the pre-planning phases, certain exploratory drillholes could be located and then outfitted with a simple communication link which would remain compatible even with the continuing evolution of communication systems. These links, whose locations would be accurately recorded, would be exposed by continuous miners during mine development thereby allowing an underground phone to be connected to a surface station in the event of an emergency. A latent network of these communication links could be installed for less than {dollar}500 each, without affecting drilling and grouting operations, and could be designed to be compatible with several communication systems as well as meeting MSHA and State requirements. This thesis examines appropriate methods and materials for incorporating an embedded communication link during pre-mine exploration drilling and addresses significant factors affecting its implementation. A design based on the research is presented

A study of spatial data models and their application to selecting information from pictorial databases

People have always used visual techniques to locate information in the space surrounding them. However with the advent of powerful computer systems and user-friendly interfaces it has become possible to extend such techniques to stored pictorial information. Pictorial database systems have in the past primarily used mathematical or textual search techniques to locate specific pictures contained within such databases. However these techniques have largely relied upon complex combinations of numeric and textual queries in order to find the required pictures. Such techniques restrict users of pictorial databases to expressing what is in essence a visual query in a numeric or character based form. What is required is the ability to express such queries in a form that more closely matches the user's visual memory or perception of the picture required. It is suggested in this thesis that spatial techniques of search are important and that two of the most important attributes of a picture are the spatial positions and the spatial relationships of objects contained within such pictures. It is further suggested that a database management system which allows users to indicate the nature of their query by visually placing iconic representations of objects on an interface in spatially appropriate positions, is a feasible method by which pictures might be found from a pictorial database. This thesis undertakes a detailed study of spatial techniques using a combination of historical evidence, psychological conclusions and practical examples to demonstrate that the spatial metaphor is an important concept and that pictures can be readily found by visually specifying the spatial positions and relationships between objects contained within them

The Apollo spacecraft: A chronology, volume 3, 1 October 1964 - 20 January 1966

The development of the Apollo spacecraft is traced along with that of Saturn V. Emphasis is placed on the detailed engineering design and exhaustive testing performed to qualify both the command and service modules and the lunar module for manned flight