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472
Routing with Guaranteed Delivery in ad hoc Wireless Networks
, 2001
"... We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of ..."
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Cited by 849 (80 self)
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We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication
Robust Distributed Network Localization with Noisy Range Measurements
, 2004
"... This paper describes a distributed, lineartime algorithm for localizing sensor network nodes in the presence of range measurement noise and demonstrates the algorithm on a physical network. We introduce the probabilistic notion of robust quadrilaterals as a way to avoid flip ambiguities that otherw ..."
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Cited by 403 (20 self)
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that otherwise corrupt localization computations. We formulate the localization problem as a twodimensional graph realization problem: given a planar graph with approximately known edge lengths, recover the Euclidean position of each vertex up to a global rotation and translation. This formulation is applicable
A NearOptimal Planarization Algorithm
, 2013
"... The problem of testing whether a graph is planar has been studied for over half a century, and is known to be solvable in O(n) time using a myriad of different approaches and techniques. Robertson and Seymour established the existence of a cubic algorithm for the more general problem of deciding whe ..."
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Cited by 2 (0 self)
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The problem of testing whether a graph is planar has been studied for over half a century, and is known to be solvable in O(n) time using a myriad of different approaches and techniques. Robertson and Seymour established the existence of a cubic algorithm for the more general problem of deciding
NearOptimal Distributed Tree Embedding
"... Tree embeddings are a powerful tool in the area of graph approximation algorithms. Roughly speaking, they transform problems on general graphs into much easier ones on trees. Fakcharoenphol, Rao, and Talwar (FRT) [STOC’04] present a probabilistic tree embedding that transforms nnode metrics into (p ..."
How Not to Characterize Planaremulable Graphs
, 2011
"... We investigate the question of which graphs have planar emulators (a locallysurjective homomorphism from some finite planar graph)—a problem raised in Fellows ’ thesis (1985) and conceptually related to the better known planar cover conjecture by Negami (1986). For over two decades, the planar em ..."
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We investigate the question of which graphs have planar emulators (a locallysurjective homomorphism from some finite planar graph)—a problem raised in Fellows ’ thesis (1985) and conceptually related to the better known planar cover conjecture by Negami (1986). For over two decades, the planar
Many distances in planar graphs
 In SODA ’06: Proc. 17th Symp. Discrete algorithms
, 2006
"... We show how to compute in O(n 4/3 log 1/3 n+n 2/3 k 2/3 logn) time the distance between k given pairs of vertices of a planar graph G with n vertices. This improves previous results whenever (n/logn) 5/6 ≤ k ≤ n 2 /log 6 n. As an application, we speed up previous algorithms for computing the dilatio ..."
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Cited by 20 (3 self)
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We show how to compute in O(n 4/3 log 1/3 n+n 2/3 k 2/3 logn) time the distance between k given pairs of vertices of a planar graph G with n vertices. This improves previous results whenever (n/logn) 5/6 ≤ k ≤ n 2 /log 6 n. As an application, we speed up previous algorithms for computing
NearOptimal Connectivity Encoding of 2Manifold Polygon Meshes
, 2002
"... ... this paper we introduce a connectivity encoding method which extends these ideas to 2manifold meshes consisting of faces with arbitrary degree. The encoding algorithm exploits duality by applying valence enumeration to both the primal and dual mesh in a symmetric fashion. It generates two sequen ..."
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Cited by 52 (7 self)
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earlier coders, sometimes as large as 50%. Remarkably, we even slightly gain over coders specialized to triangle or quad meshes. A theoretical analysis reveals that our approach is nearoptimal as we achieve the Tutte entropy bound for arbitrary planar graphs of 2 bits per edge in the worst case.
Geometric Spanner for Routing in Mobile Networks
, 2001
"... Abstract—We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) be ..."
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Cited by 183 (18 self)
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Abstract—We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2
Exact Distance Oracles for Planar Graphs
, 2010
"... We provide the first linearspace data structure with provable sublinear query time for exact pointtopoint shortest path queries in planar graphs. We prove that for any planar graph G with nonnegative arc lengths and for any ɛ> 0 there is a data structure that supports exact shortest path and d ..."
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Cited by 9 (5 self)
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for any shortestpath data structure for planar graphs with space S = o(n 4/3 lg 1/3 n). As a consequence, we also obtain an algorithm that computes k–many distances in planar graphs in time O((kn) 2/3 (lg n) 2 (lg lg n) −1/3 + n(lg n) 2 / lg lg n). 1
Results 1  10
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472