Half-Guarding Weakly-Visible Polygons and Terrains

We consider a variant of the art gallery problem where all guards are limited to seeing 180degree. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for vertex guarding the vertices of a weakly-visible polygon with half-guards. We extend this to vertex guarding the boundary of a weakly-visible polygon with half-guards. We also show NP-hardness for vertex guarding a weakly-visible polygon with half-guards. Lastly, we show that the orientation of half-guards is critical in terrain guarding. Depending on the orientation of the half-guards, the problem is either very easy (polynomial time solvable) or very hard (NP-hard)

Vertex-Edge Pseudo-Visibility Graphs: Characterization and Recognition

We extend the notion of polygon visibility graphs to pseudo-polygons defined on generalized configurations of points. We consider both vertex-to-vertex, as well as vertex-to-edge visibility in pseudo-polygons. We study the characterization and recognition problems for vertex-edge pseudo-visibility graphs. Given a bipartite graph G satisfying three simple properties, which can all be checked in polynomial time, we show that we can define a generalized configuration of points and a pseudo-polygon on it, so that its vertex-edge pseudo-visibility graph is G. This provides a full characterization of vertex-edge pseudo-visibility graphs and a polynomial-time algorithm for the decision problem. It also implies that the decision problem for vertex visibility graphs of pseudo-polygons is in NP (as opposed to the same problem with straight-edge visibility, which is only known to be in PSPACE)

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Control for Localization and Visibility Maintenance of an Independent Agent using Robotic Teams

Given a non-cooperative agent, we seek to formulate a control strategy to enable a team of robots to localize and track the agent in a complex but known environment while maintaining a continuously optimized line-of-sight communication chain to a fixed base station. We focus on two aspects of the problem. First, we investigate the estimation of the agent\u27s location by using nonlinear sensing modalities, in particular that of range-only sensing, and formulate a control strategy based on improving this estimation using one or more robots working to independently gather information. Second, we develop methods to plan and sequence robot deployments that will establish and maintain line-of-sight chains for communication between the independent agent and the fixed base station using a minimum number of robots. These methods will lead to feedback control laws that can realize this plan and ensure proper navigation and collision avoidance

Studies on Kernels of Simple Polygons

The kernel of a simple polygon is the set of points in its interior from which all points inside the polygon are visible. We formally establish that for a given convex polygon Q we can always construct a larger simple polygon with many reflex vertices such that Q is the kernel of P. We present algorithms for decomposing a strongly monotone polygon into star-polygons. This decomposition is applied for developing an efficient algorithm for placing a small number of vertical towers to cover the entire given 1.5D terrain. We also present an experimental investigation of the proposed algorithm. The implementation is done in the Java programming language and the resulting prototype supports a user-friendly interface

Scoring, selecting, and developing physical impact models for multi-hazard risk assessment

This study focuses on scoring, selecting, and developing physical fragility (i.e., the probability of reaching or exceeding a certain DS given a specific hazard intensity) and/or vulnerability (i.e., the probability of impact given a specific hazard intensity) models for assets, with particular emphasis on buildings. Given a set of multiple relevant hazards for a selected case-study region, the proposed procedure involves 1) mapping the relevant asset classes (i.e., construction types for a given occupancy) in the region to a set of existing candidate fragility, vulnerability and/or damage-to-impact models, also accounting for specific modelling requirements (e.g., time dependency due to ageing/deterioration of buildings, multi-hazard interactions); 2) scoring the candidate models according to relevant criteria to select the most suitable ones for a given application; or 3) using state-of-the-art numerical or empirical methods to develop fragility/vulnerability models not already available. The approach is demonstrated for the buildings of the virtual urban testbed “Tomorrowville”, considering earthquakes, floods, and debris flows as case-study hazards

Historical Change of Seagrasses in the Mississippi and Chandeleur Sounds

Seagrasses are important coastal resources facing numerous stressors, and losses have been documented from local to global assessments. Under the broad theme of habitat loss and fragmentation, a study of historical change in total area and landscape configuration of seagrasses in the Mississippi and Chandeleur Sounds was conducted. Mapping data was collated from a multitude of previous projects from 1940 to 2011. Comparisons of seagrass area among various studies that used different mapping methods can result in overestimation of area change and misleading conclusions of change over time. The vegetated seagrass area (VSA) data were generalized to a common resolution for further analysis. Spatial configuration of the seagrass landscape was examined through: (1) an exploratory spatial data analysis using seagrass patch size distribution and hot spot analysis, and (2) a core set of seagrass landscape FRAGSTATS metrics and a principal component analysis to identify major pattern. This study demonstrated a comprehensive analysis across spatial and temporal scales and used multiple landscape indices (from habitat, species composition, VSA, patch size distribution, to spatial configuration at patch- and landscape-levels) to provide insights on the pattern and dynamics of the seagrass landscape. A conceptual model of seagrass landscape change based on two principal factors, overall landscape lushness and continuity, was proposed for the Mississippi Sound. Overall the study area lost seagrasses with contracted spatial extent over the 71-year period, ostensibly due to loss or reduction of protective island barriers and reductions in water quality. The seagrass landscape in the Mississippi Sound exhibited signs of area loss and fragmentation as far back as the 1940-1950s. The landscape in the 1970s was characterized by loss of habitat, loss of seagrass species, the lowest VSA, a faster rate of decline and a higher loss in VSA than before 1970, a low proportion of large-sized patches and their low contribution to VSA, a reduced intensity of hot spots, and a high degree of fragmentation. Recovery of seagrass occurred during the 1980s and 1990s, with the landscape exhibiting characteristics of a more contiguous and more vegetated condition throughout the early 2000s