Results 1  10
of
205
LinearTime Algorithms for Holefree Rectilinear Proportional Contact Graph Representations
"... In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we first study proportional contact representation ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algorithm for proportional contact representation of a maximal planar graph uses 12sided rectilinear polygons and takes O(n log n) time. We describe a new algorithm that guarantees 10sided
LinearTime Algorithms for Rectilinear Holefree Proportional Contact Representations
"... A proportional contact representation of a planar graph is one where each vertex is represented by a simple polygon with area proportional to a given weight and adjacencies between polygons represent edges between the corresponding pairs of vertices. In this paper we study proportional contact rep ..."
Abstract
 Add to MetaCart
that produces a holefree proportional contact representation of a maximal planar graph with a 10sided rectilinear polygons. For a planar 3tree we give a lineartime algorithm for a holefree proportional contact representation with 8sided rectilinear polygons. Furthermore, there exist a planar 3tree
A Rectilinearity Measurement for Polygons
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... In this paper we define a function 7g(P) which is defined for any polygon P and which maps a given polygon P into a number from the interval (0, 1]. The number 7g(P) can be used as an estimate of the rectilinearity of P. The mapping 7(P) has the following desirable properties:  any polygon P h ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
In this paper we define a function 7g(P) which is defined for any polygon P and which maps a given polygon P into a number from the interval (0, 1]. The number 7g(P) can be used as an estimate of the rectilinearity of P. The mapping 7(P) has the following desirable properties:  any polygon P
Rectilinearity measurements for polygons
 IEEE Trans. on Patt. Anal. and Mach. Intell
"... The paper introduces a shape measure intended to describe the extent to which a closed polygon is rectilinear. Other than somewhat obvious measures of rectilinearity (e.g. the sum of the differences of each corner’s angle from 90◦) there has been little work in deriving a measure that is straightfor ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
The paper introduces a shape measure intended to describe the extent to which a closed polygon is rectilinear. Other than somewhat obvious measures of rectilinearity (e.g. the sum of the differences of each corner’s angle from 90◦) there has been little work in deriving a measure
Lineartime algorithms for proportional contact graph representations
, 2011
"... Abstract. In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representat ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algorithm for proportional contact representation of a maximal planar graph uses 12sided rectilinear polygons and takes�time. We describe a new algorithm that guarantees 10sided rectilinear polygons
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
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
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. ..."
Abstract

Cited by 26 (1 self)
 Add to MetaCart
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.
Results 1  10
of
205