Minimum K-partitioning of rectilinear polygons

Generalized Guarding and Partitioning for Rectilinear Polygons

Minimum Rectilinear Polygons for Given Angle Sequences

In this paper, we consider the problem of computing, for a given rectilinear angle sequence, a “small” rectilinear polygon. A rectilinear angle sequence S is a sequence of left (90◦) turns and right (270◦) turns, that is, S = (s1, . . . , sn) ∈ {L, R}, where n is the length of S. As we consider only rectilinear angle sequences, we usually drop the term “rectilinear.” A polygon P realizes an ang...

Computing Partitions of Rectilinear Polygons with Minimum Stabbing Number

The stabbing number of a partition of a rectilinear polygon P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment contained in P . We consider the problem of finding a rectangular partition with minimum stabbing number for a given rectilinear polygon P . First, we impose a conforming constraint on partitions: every vertex of every rectangle in the parti...

Minimum rectangular partition problem for simple rectilinear polygons

In this paper, an O ( n log log n ) algorithm is proposed for minimally rectangular partitioning a simple rectilinear polygon. For any simple rectilinear polygon P , a vertex-edge visible pair is a vertex and an edge that can be connected by a horizontal or vertical line segment that lies entirely inside P . We show that, if the vertex-edge visible pairs are found, the maximum matching and the ...

Evacuation 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...