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341
Approximating the diameter of planar graphs in near linear time
 In Proc. ICALP
, 2013
"... We present a (1 + ε)approximation algorithm running in O( f (ε) · n log 4 n) time for finding the diameter of an undirected planar graph with n vertices and with nonnegative edge lengths. ..."
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Cited by 1 (0 self)
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We present a (1 + ε)approximation algorithm running in O( f (ε) · n log 4 n) time for finding the diameter of an undirected planar graph with n vertices and with nonnegative edge lengths.
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul
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
Subgraph Isomorphism in Planar Graphs and Related Problems
, 1999
"... We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used to ..."
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Cited by 150 (2 self)
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We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time
 In Proc. 42nd IEEE Annual Symposium on Foundations of Computer Science
, 2001
"... for finding shortest paths in a planar graph with real weights. ..."
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Cited by 69 (0 self)
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for finding shortest paths in a planar graph with real weights.
Approximate Tree Decompositions of Planar Graphs in Linear Time
"... Many algorithms have been developed for NPhard problems on graphs with small treewidth k. For example, all problems that are expressible in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth. It turns out that the bottleneck of many algorithms for NPha ..."
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Cited by 5 (0 self)
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hard problems is the computation of a tree decomposition of width O(k). In particular, by the bidimensional theory, there are many linear extended monadic second order problems that can be solved on nvertex planar graphs with treewidth k in a time linear in n and subexponential in k if a tree decomposition
PolynomialTime Approximation Schemes for Geometric Graphs
, 2001
"... A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weigh ..."
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Cited by 102 (5 self)
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A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total
Nearlinear time construction of sparse neighborhood covers
 SIAM JOURNAL ON COMPUTING
, 1998
"... This paper introduces a nearlinear time sequential algorithm for constructing a sparse neighborhood cover. This implies analogous improvements (from quadratic to nearlinear time) for any problem whose solution relies on network decompositions, including small edge cuts in planar graphs, approximat ..."
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Cited by 49 (4 self)
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This paper introduces a nearlinear time sequential algorithm for constructing a sparse neighborhood cover. This implies analogous improvements (from quadratic to nearlinear time) for any problem whose solution relies on network decompositions, including small edge cuts in planar graphs
NearLinear Time ConstantFactor Approximation Algorithm for BranchDecomposition of Planar Graphs
"... ar ..."
Approximations for the Disjoint Paths Problem in HighDiameter Planar Networks
, 1995
"... We consider the problem of connecting distinguished terminal pairs in a graph via edgedisjoint paths. This is a classical NPcomplete problem for which no general approximation techniques are known; it has recently been brought into focus in papers discussing applications to admission control in hig ..."
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Cited by 50 (5 self)
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in highspeed networks and to routing in alloptical networks. In this paper we provide O(log n)approximation algorithms for two natural optimization versions of this problem for the class of nearlyEulerian, uniformly highdiameter planar graphs, which includes twodimensional meshes and other common
Results 1  10
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341