Guard placement for efficient pointin-polygon proofs

{eppstein, goodrich, nodari} (at) ics.uci.edu We consider the problem of placing a small number of angle guards inside a simple polygon P so as to provide efficient proofs that any given point is inside P. Each angle guard views an infinite wedge of the plane, and a point can prove membership in P if it is inside the wedges for a set of guards whose common intersection contains no points outside the polygon. This model leads to a broad class of new art gallery type problems, which we call “sculpture garden ” problems and for which we provide upper and lower bounds. In particular, we show there is a polygon P such that a “natural” angle-guard vertex placement cannot fully distinguish between points on the inside and outside of P (even if we place a guard at every vertex of P), which implies that Steinerpoint guards are sometimes necessary. More generally, we show that, for any polygon P, there is a set of n + 2(h − 1) angle guards that solve the sculpture garden problem for P, where h is the number of holes in P (so a simple polygon can be defined with n − 2 guards). In addition, we show that, for any orthogonal polygon P, the sculpture garden problem can be solved using n angle guards. We also give an 2 example of a class of simple (non-general-position) polygons that have sculpture garden solutions using O ( √ n) guards, and we show this bound is optimal to within a constant factor. Finally, while optimizing the number of guards solving a sculpture garden problem for a particular P is of unknown complexity, we show how to find in polynomial time a guard placement whose size is within a factor of 2 of the optimal number for any particular polygon

Subclass Discriminant Analysis of Morphological and Textural Features for HEp-2 Staining Pattern Classification

Classifying HEp-2 fluorescence patterns in Indirect Immunofluorescence (IIF) HEp-2 cell imaging is important for the differential diagnosis of autoimmune diseases. The current technique, based on human visual inspection, is time-consuming, subjective and dependent on the operator's experience. Automating this process may be a solution to these limitations, making IIF faster and more reliable. This work proposes a classification approach based on Subclass Discriminant Analysis (SDA), a dimensionality reduction technique that provides an effective representation of the cells in the feature space, suitably coping with the high within-class variance typical of HEp-2 cell patterns. In order to generate an adequate characterization of the fluorescence patterns, we investigate the individual and combined contributions of several image attributes, showing that the integration of morphological, global and local textural features is the most suited for this purpose. The proposed approach provides an accuracy of the staining pattern classification of about 90%

Optimal Constrained Wireless Emergency Network Antennae Placement

With increasing number of mobile devices, newly introduced smart devices, and the Internet of things (IoT) sensors, the current microwave frequency spectrum is getting rapidly congested. The obvious solution to this frequency spectrum congestion is to use millimeter wave spectrum ranging from 6 GHz to 300 GHz. With the use of millimeter waves, we can enjoy very high communication speeds and very low latency. But, this technology also introduces some challenges that we hardly faced before. The most important one among these challenges is the Line of Sight (LOS) requirement. In the emergent concept of smart cities, the wireless emergency network is set to use millimeter waves. We have worked on the problem of efficiently finding a line of sight for such wireless emergency network antennae in minimal time. We devised two algorithms, Sequential Line of Sight (SLOS) and Tiled Line of Sight (TLOS), both perform better than traditional algorithms in terms of execution time. The tiled line of sight algorithm reduces the time required for a single line of sight query from 200 ms for traditional algorithms to mere 1.7 ms on average

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

Energy-Efficient 3D Deployment of Aerial Access Points in a UAV Communication System

In this letter, we propose an energy-efficient 3-dimensional placement of multiple aerial access points (AAPs), in the desired area, acting as flying base stations for uplink communication from a set of ground user equipment (UE). The globally optimal energy-efficient vertical position of AAPs is derived analytically by considering the inter-cell interference and AAP energy consumption. The horizontal position of AAPs which maximize the packing density of the AAP coverage area are determined using a novel regular polygon-based AAP placement algorithm. We also determine the maximum number of non-interfering AAPs that can be placed in the desired area. The effect of the AAP energy consumption on the optimal placement and the analytic findings are verified via numerical simulations.Comment: This version of the work has been accepted for publication in the IEEE COMMUNICATIONS LETTERS. 6 pages; 5 figure