
Geometric Embedding of Path and Cycle Graphs in Pseudoconvex Polygons
Given a graph G with n vertices and a set S of n points in the p...
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Exact and Approximation Algorithms for ManyToMany Point Matching in the Plane
Given two sets S and T of points in the plane, of total size n, a manyt...
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A universal predictorcorrector type incremental algorithm for the construction of weighted straight skeletons based on the notion of deforming polygon
A new predictorcorrector type incremental algorithm is proposed for the...
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A linear algorithm for Brick Wang tiling
The Wang tiling is a classical problem in combinatorics. A major theoret...
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Minimum Cuts in Geometric Intersection Graphs
Let 𝒟 be a set of n disks in the plane. The disk graph G_𝒟 for 𝒟 is the ...
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The SetMaxima Problem in a Geometric Setting
In this paper we look at the classical setmaxima problem. We give a new...
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A Distance Function for Comparing StraightEdge Geometric Figures
This paper defines a distance function that measures the dissimilarity b...
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Linear Size Planar Manhattan Network for Convex Point Sets
Let G = (V, E) be an edgeweighted geometric graph such that every edge is horizontal or vertical. The weight of an edge uv ∈ E is its length. Let W_G (u,v) denote the length of a shortest path between a pair of vertices u and v in G. The graph G is said to be a Manhattan network for a given point set P in the plane if P ⊆ V and ∀ p,q ∈ P, W_G (p,q)=pq_1. In addition to P, graph G may also include a set T of Steiner points in its vertex set V. In the Manhattan network problem, the objective is to construct a Manhattan network of small size for a set of n points. This problem was first considered by Gudmundsson et al.<cit.>. They give a construction of a Manhattan network of size Θ(n log n) for general point set in the plane. We say a Manhattan network is planar if it can be embedded in the plane without any edge crossings. In this paper, we construct a linear size planar Manhattan network for convex point set in linear time using O(n) Steiner points. We also show that, even for convex point set, the construction in Gudmundsson et al. <cit.> needs Ω (n log n) Steiner points and the network may not be planar.
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