منابع مشابه
Open Guard Edges and Edge Guards in Simple Polygons
An open edge of a simple polygon is the set of points in the relative interior of an edge. We revisit several art gallery problems, previously considered for closed edge guards, using open edge guards. A guard edge of a polygon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon admits at most one open guard edge, and give a simple new proof tha...
متن کاملGuarding simple polygons with semi-open edge guards
Let bd(P ) denote the boundary of a simple polygon P . Points p and q of P are mutually visible if segment pq lies entirely inside P . This notion of visibility gave birth to an extensive literature on art-gallery problems [3], concerned with guarding the floor of a polygonal art-gallery. Chvatal [2] showed that bn/3c point guards are always sufficient and sometimes necessary. Allowing guards t...
متن کاملEvacuation of Rectilinear Polygons
We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the “confluent” context in which the routes to exits remain fixed over time, and the “non-confluent” context in which routes may change. Confluent evacuation plans are simpler to carry out, as they allo...
متن کاملHidden Mobile Guards in Simple Polygons
We consider guarding classes of simple polygons using mobile guards (polygon edges and diagonals) under the constraint that no two guards may see each other. In contrast to most other art gallery problems, existence is the primary question: does a specific type of polygon admit some guard set? Types include simple polygons and the subclasses of orthogonal, monotone, and starshaped polygons. Add...
متن کاملCompetitive Exploration of Rectilinear Polygons
Exploring a polygon with robots when the robots do not have knowledge of the surroundings can be viewed as an online problem. Typical for online problems is that decisions must be made based on past events without complete information about the future. In our case the robots do not have complete information about the environment. Competitive analysis can be used to measure the performance of me...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 1998
ISSN: 0925-7721
DOI: 10.1016/s0925-7721(98)00024-8