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128
Ramified rectilinear polygons: coordinatization by dendrons
, 2010
"... Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic l1metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectang ..."
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Cited by 5 (4 self)
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Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic l1metric is thus inherited from the product of the two finite dendrons via an isometric embedding
Evacuation of rectilinear polygons
 In Combinatorial Optimization and Applications
, 2010
"... Abstract. 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 “nonconf ..."
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Cited by 2 (0 self)
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Abstract. 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
Covering Rectilinear Polygons with AxisParallel Rectangles
, 2003
"... We give an O ( log n) factor approximation algorithm for covering a rectilinear polygon with holes using axisparallel rectangles. This is the first polynomial time approximation algorithm for this problem with an o(log n) approximation factor. ..."
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Cited by 26 (1 self)
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We give an O ( log n) factor approximation algorithm for covering a rectilinear polygon with holes using axisparallel rectangles. This is the first polynomial time approximation algorithm for this problem with an o(log n) approximation factor.
Complexities of Efficient Solutions of Rectilinear Polygon Cover Problems
, 1994
"... The rectilinear polygon cover problem is one in which a certain class of features of a rectilinear polygon of n vertices has to be covered with the minimum number of rectangles included in the polygon. In particular, we consider covering the entire interior, the boundary and the set of corners of th ..."
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Cited by 13 (1 self)
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The rectilinear polygon cover problem is one in which a certain class of features of a rectilinear polygon of n vertices has to be covered with the minimum number of rectangles included in the polygon. In particular, we consider covering the entire interior, the boundary and the set of corners
Extending Rectangle Join Algorithms for Rectilinear Polygons
 In Proc. Int. Conf. on WebAge Information Management
, 2000
"... Spatial joins are very important but costly operations in spatial databases. A typical evaluation strategy of spatial joins is to perform the join on approximations of spatial objects and then evaluate the join of the real objects based on the results. The common approximation is the minimum boundin ..."
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Cited by 5 (4 self)
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bounding rectangle. Minimum bounding rectangles are coarse approximations of spatial objects and may cause a large number of "false hits". In this paper, we consider a more general form of approximation with rectilinear polygons for spatial objects in the context of spatial join evaluation. A
Computing Partitions of Rectilinear Polygons with Minimum Stabbing Number?
"... Abstract. The stabbing number of a partition of a rectilinear polygon P into rectangles is the maximum number of rectangles stabbed by any axisparallel line segment contained in P. We consider the problem of finding a rectangular partition with minimum stabbing number for a given rectilinear polygo ..."
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Cited by 1 (1 self)
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Abstract. The stabbing number of a partition of a rectilinear polygon P into rectangles is the maximum number of rectangles stabbed by any axisparallel line segment contained in P. We consider the problem of finding a rectangular partition with minimum stabbing number for a given rectilinear
Fast Algorithms To Partition Simple Rectilinear Polygons*
"... Two algorithms to partition holefree rectilinear polygons are developed. One has complexity ∼ O(kn) and the other O(nlogk) where n is the number of vertices in the polygon and k is the smaller of the number of vertical and horizontal inversions of the polygon. k is a measure of the simplicity of a ..."
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Cited by 1 (0 self)
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Two algorithms to partition holefree rectilinear polygons are developed. One has complexity ∼ O(kn) and the other O(nlogk) where n is the number of vertices in the polygon and k is the smaller of the number of vertical and horizontal inversions of the polygon. k is a measure of the simplicity of a
The Art Gallery Theorem for Rectilinear Polygons with Holes
, 1994
"... It is proved that any rectilinear polygon on n vertices, possibly with holes, can be partitioned into at most \Xi n 4 \Pi rectilinear stars each of size at most 12. *Institut fur Informatik, Freie Universitat Berlin, Takustr. 9, D14195 Berlin, hoffmann@tcs.fuberlin.de, Supported by the ESPRI ..."
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It is proved that any rectilinear polygon on n vertices, possibly with holes, can be partitioned into at most \Xi n 4 \Pi rectilinear stars each of size at most 12. *Institut fur Informatik, Freie Universitat Berlin, Takustr. 9, D14195 Berlin, hoffmann@tcs.fuberlin.de, Supported
Results 1  10
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128