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87
Rectilinear Shortest Path and Rectilinear Minimum Spanning Tree with Neighborhoods
"... Abstract. We consider a setting where we are given a graph G = (R, E), where R = {R1,..., Rn} is a set of polygonal regions in the plane. Placing a point pi inside each region Ri turns G into an edgeweighted graph Gp, p = {p1,..., pn}, where the cost of (Ri, Rj) ∈ E is the distance between pi and ..."
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Abstract. We consider a setting where we are given a graph G = (R, E), where R = {R1,..., Rn} is a set of polygonal regions in the plane. Placing a point pi inside each region Ri turns G into an edgeweighted graph Gp, p = {p1,..., pn}, where the cost of (Ri, Rj) ∈ E is the distance between pi
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 ..."
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and runs in time. We also describe a lineartime algorithm for proportional contact representation of planar 3trees with 8sided rectilinear polygons and show that this optimal, as there exist planar 3trees that requires 8sided polygons. Finally, we show that a maximal outerplanar graph admits a
Hamiltonian triangulations for . . .
"... Highperformance rendering engines in computer graphics are often pipelined, and their speed is bounded by the rate at which triangulation data can be sent into the machine. To reduce the data rate, it is desirable to order the triangles so that consecutive triangles share a face, meaning that only ..."
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in the plane do not admit a sequential triangulation. Further, we give e cient algorithms for testing whether a given triangulation of a point set or polygon is sequential. Show how to test whether a given polygon P has a Hamiltonian triangulation in time linear in the size of its visibility graph, and show
On sequential triangulations of simple polygons
 In Proceedings of the 16 th Canadian Conference on Computational Geometry
, 1996
"... Abstract A triangulation is said to be Hamiltonian if its dualgraph contains a Hamiltonian path. A sequential triangulation is a Hamiltonian triangulation having the additional property that the "turns " in the Hamiltonian path alternate left/right. Such triangulations are usefuli ..."
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Cited by 1 (0 self)
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the polygon's visibility graph and hence runs in worse case O(n2) time [1].
Connected Proper Interval Graphs and the Guard Problem in Spiral Polygons
, 1995
"... this paper is to study the hamiltonicity of proper interval graphs and applications of these graphs to the guard problem in spiral polygons. The Hamiltonian path (circuit) problem is, given an undirected graph G = (V ,E), to determine whether G contains a Hamiltonian path (circuit). These two proble ..."
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this paper is to study the hamiltonicity of proper interval graphs and applications of these graphs to the guard problem in spiral polygons. The Hamiltonian path (circuit) problem is, given an undirected graph G = (V ,E), to determine whether G contains a Hamiltonian path (circuit). These two
On the Hardness of TurnAngleRestricted Rectilinear Cycle Cover Problems (Extended Abstract)
, 2002
"... A cycle cover of a graph G is a collection of disjoint cycles that spans G. Generally, a (possibly disconnected) cycle cover is easier to construct than a connected (Hamiltonian) cycle cover. One might expect this since the cycle cover property is local whereas connectivity is a global constraint. ..."
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A cycle cover of a graph G is a collection of disjoint cycles that spans G. Generally, a (possibly disconnected) cycle cover is easier to construct than a connected (Hamiltonian) cycle cover. One might expect this since the cycle cover property is local whereas connectivity is a global constraint
A class of shellable segment scenes with Hamiltonian visibility graphs
"... We prove that the visibility graph of a set of line segments lying in disjoint vertical strips contains a monotone circumscribing Hamiltonian cycle. This provides some evidence for a conjecture of Mirzaian, as refined by O'Rourke and Rippel. Keywords: visibility graphs; Hamiltonian cycles A se ..."
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graph of a segment scene is always Hamiltonian. Of special interest are simple Hamiltonian cycles, i.e., cycles that are simple polygons; and also circumscribing Hamiltonian cycles, i.e., simple Hamiltonian cycles containing all segments of the scene in their interior. Mirzaian [1] also conjectured
QuarterT\rrns and Hamiltonian Cycles for Annular Chessknight Graphs.
"... Abstract. In this article, we discuss some aspects of the search for chessknight closed tours in a chessboard, as in [1], [g], [10], [14] and [16] and give an elementary application to the interaction between graph theory and group theory. These closed tours will be herewith denoted as chessknight H ..."
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as centered at the origin in I and with their sides respectively parallel to the coordinate axes. Graph vertices are taken to be the chess entry centers. Then, if n is an integer larger than 1, the n x nchessboard is identified with the vertex setya {r'(n1)12l"i(")l €Z,for i:0,1}. Givenl
A Triangulation for Optimal Strip Decomposition in Simple Polygons
"... In computer graphics, most polygonal surfaces are rendered via triangles. Rendering a set of triangles needs the data of the triangle vertices. Since the speed of rendering is bounded by data rate, reducing the amount of data will make rendering faster. This can be attained by ordering triangles so ..."
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that consecutive triangles share an edge, that is, only one additional vertex need to be transmitted to describe each triangle. There exists such an order if and only if the dual graph of the triangulation contains a Hamiltonian path. Many polygons, however, do not have Hamiltonian triangulation; they can
Micronuclear Sequences Associated with Assembly Graphs
, 2011
"... This paper investigates given an assembly graph, find the possible micronuclear sequences in terms of MDSs and IESs; which represent Hamiltonian polygonal paths. We will consider the orientations of the assembly graph and Hamiltonian polygonal path. To obtain a micronuclear sequence of this path, we ..."
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This paper investigates given an assembly graph, find the possible micronuclear sequences in terms of MDSs and IESs; which represent Hamiltonian polygonal paths. We will consider the orientations of the assembly graph and Hamiltonian polygonal path. To obtain a micronuclear sequence of this path
Results 11  20
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87