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Computing Cartograms with Optimal Complexity
"... In a rectilinear dual of a planar graph vertices are represented by simple rectilinear polygons and edges are represented by sidecontact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each region is equal to a prespecified weight of the corresponding ve ..."
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Cited by 8 (7 self)
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compute the cartograms in linear time. Moreover, we prove that even for Hamiltonian graphs 8sided rectilinear polygons are necessary, by constructing a nontrivial lower bound example. The complexity of the cartograms can be reduced to 6 if the Hamiltonian path has the extra property that it is one
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
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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. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4cycles or paths of length at most 3
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 ..."
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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
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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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
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 ..."
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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
The Steiner Tree Problem for Terminals on the Boundary of a Rectilinear Polygon
 In Proc. of the DIMACS Workshop on Network Design: Connectivity and Facilities Location
, 1997
"... Given a simple rectilinear polygon P with k sides and n terminals on its boundary, we present an O(k 3 n)time algorithm to compute the minimal rectilinear Steiner tree lying inside P interconnecting the terminals. We obtain our result by proving structural properties of a selective set of minimal ..."
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Given a simple rectilinear polygon P with k sides and n terminals on its boundary, we present an O(k 3 n)time algorithm to compute the minimal rectilinear Steiner tree lying inside P interconnecting the terminals. We obtain our result by proving structural properties of a selective set
Results 1  10
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24,370