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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
An approximation algorithm for complete partition of regular graphs
, 2004
"... A complete partition of a graph is a partition of the vertex set such that any two classes are connected by an edge. We consider the problem of finding a complete partition maximizing the number of classes. This relates to clustering into the greatest number of groups so as to minimize the diameter ..."
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Cited by 2 (1 self)
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A complete partition of a graph is a partition of the vertex set such that any two classes are connected by an edge. We consider the problem of finding a complete partition maximizing the number of classes. This relates to clustering into the greatest number of groups so as to minimize the diameter
Subcubic Equivalences Between Graph Centrality Problems, APSP and Diameter
"... Measuring the importance of a node in a network is a major goal in the analysis of social networks, biological systems, transportation networks etc. Different centrality measures have been proposed to capture the notion of node importance. For example, the center of a graph is a node that minimizes ..."
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Cited by 2 (1 self)
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of a single node take roughly cubic time in the number n of nodes in the input graph. It is open whether these problems admit truly subcubic algorithms, i.e. algorithms with running time Õ(n3−δ) for some constant δ> 01. We relate the complexity of the mentioned centrality problems to two classical
10. Tight Bounds for Distributed Selection
 7th IEEE International Conference on PeertoPeer Computing (P2P
, 2007
"... We revisit the problem of distributed kselection where, given a general connected graph of diameter D consisting of n nodes in which each node holds a numeric element, the goal is to determine the k th smallest of these elements. In our model, there is no imposed relation between the magnitude of t ..."
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Cited by 16 (4 self)
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We revisit the problem of distributed kselection where, given a general connected graph of diameter D consisting of n nodes in which each node holds a numeric element, the goal is to determine the k th smallest of these elements. In our model, there is no imposed relation between the magnitude
Minimizing the diameter of a network using shortcut edges
 IN ALGORITHM THEORY  SWAT 2010
, 2010
"... We study the problem of minimizing the diameter of a graph by adding k shortcut edges, for speeding up communication in an existing network design. We develop constantfactor approximation algorithms for different variations of this problem. We also show how to improve the approximation ratios usin ..."
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Cited by 6 (0 self)
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We study the problem of minimizing the diameter of a graph by adding k shortcut edges, for speeding up communication in an existing network design. We develop constantfactor approximation algorithms for different variations of this problem. We also show how to improve the approximation ratios
On the Power Assignment Problem in Radio Networks
, 2004
"... A Given a finite set S of points (i.e. the stations of a radio network) on a ddimensional Euclidean space and a positive integer 1 � h � S−1, the MIN d D hRANGE ASSIGNMENT problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided t ..."
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Cited by 63 (4 self)
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that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops. Two main issues related to this problem are considered in this paper: the tradeoff between the power consumption and the number of hops; the computational complexity of the MIN d D hRANGE ASSIGNMENT
A Lagrangian RelaxandCut Approach for the Bounded Diameter Minimum Spanning Tree Problem
, 2008
"... We consider the problem of finding for a given weighted graph a minimum cost spanning tree whose diameter does not exceed a specified upper bound. This problem is NPhard and has several applications, e.g. when designing communication networks and quality of service is of concern. We model the prob ..."
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We consider the problem of finding for a given weighted graph a minimum cost spanning tree whose diameter does not exceed a specified upper bound. This problem is NPhard and has several applications, e.g. when designing communication networks and quality of service is of concern. We model
© 2002 SpringerVerlag New York Inc. Augmenting Trees to Meet Biconnectivity and Diameter Constraints 1
"... Abstract. Given a graph G = (V, E) and a positive integer D, we consider the problem of finding a minimum number of new edges E ′ such that the augmented graph G ′ = (V, E ∪ E ′ ) is biconnected and has diameter no greater than D. In this note we show that this problem is NPhard for all fixed D, b ..."
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, by employing a reduction from the DOMINATING SET problem. We prove that the problem remains NPhard even for forests and trees, but in this case we present approximation algorithms with worstcase bounds 3 (for even D) and 6 (for odd D). A closely related problem of finding a minimum number of edges
NearOptimal Distributed Approximation of MinimumWeight Connected Dominating Set
"... This paper presents a nearoptimal distributed approximation algorithm for the minimumweight connected dominating set (MCDS) problem. We use the standard distributed message passing model called the CONGEST model in which in each round each node can send O(log n) bits to each neighbor. The presente ..."
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Cited by 3 (1 self)
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. The presented algorithm finds an O(log n) approximation in Õ(D+√n) rounds, where D is the network diameter and n is the number of nodes. MCDS is a classical NPhard problem and the achieved approximation factor O(log n) is known to be optimal up to a constant factor, unless P = NP. Furthermore, the Õ(D +√n
Results 1  10
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