منابع مشابه
Spanners for Directed Transmission Graphs
Let P ⊂ R2 be a planar n-point set such that each point p ∈ P has an associated radius rp > 0. The transmission graph G for P is the directed graph with vertex set P such that for any p, q ∈ P , there is an edge from p to q if and only if d(p, q) ≤ rp. Let t > 1 be a constant. A t-spanner for G is a subgraph H ⊆ G with vertex set P so that for any two vertices p, q ∈ P , we have dH(p, q) ≤ tdG(...
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The simplest model of a wireless network graph is the Unit Disk Graph (UDG): an edge exists in UDG if the Euclidean distance between its endpoints is ≤ 1. The problem of constructing planar spanners of Unit Disk Graphs with respect to the Euclidean distance has received considerable attention from researchers in computational geometry and ad-hoc wireless networks. In this paper, we present an a...
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In this paper, we establish a novel balanced separator theorem for Unit Disk Graphs (UDGs), which mimics the well-known Lipton and Tarjan’s planar balanced shortest paths separator theorem. We prove that, in any n-vertex UDG G, one can find two hop-shortest paths P (s, x) and P (s, y) such that the removal of the 3-hopneighborhood of these paths (i.e., N G[P (s, x)∪P (s, y)]) from G leaves no c...
متن کاملSpanners and Reachability Oracles for Directed Transmission Graphs
Let P ⊂ R be a set of n points, each with an associated radius rp > 0. The transmission graph G for P has vertex set P and an edge from p to q if and only if q lies in the ball with radius rp around p. Let t > 1. A t-spanner H for G is a sparse subgraph of G such that for any two vertices p, q connected by a path of length ` in G, there is a p-q-path of length at most t` in H. We show how to co...
متن کاملOn Geometric Spanners of Euclidean and Unit Disk Graphs
We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor Cdel ≈ 2.42; however, its degree may not be bounded. Our first result is a very simple linear time algorithm for constructing a subgraph of the Delaunay graph with stretch factor ρ = 1 + ...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2011
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-011-9580-8