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Results 1 - 10
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582
More algorithms for all-pairs shortest paths in weighted graphs
- In Proceedings of 39th Annual ACM Symposium on Theory of Computing
, 2007
"... In the first part of the paper, we reexamine the all-pairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n / log 2 n), which improves all known algorithms for general real-weighted dense graphs. In the second part of the paper, we use fast matrix multipl ..."
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Cited by 75 (3 self)
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In the first part of the paper, we reexamine the all-pairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n / log 2 n), which improves all known algorithms for general real-weighted dense graphs. In the second part of the paper, we use fast matrix
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 error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
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Cited by 676 (15 self)
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the real QMR network to converge if the priors were sampled randomly in the range [0, Small priors are not the only thing that causes oscil lation. Small weights can, too. The effect of both The exact marginals are represented by the circles; the ends of the "error bars" represent the loopy
A general approximation technique for constrained forest problems
- SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
Abstract
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Cited by 414 (21 self)
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of these problems. For instance, we obtain a 2-approximation algorithm for the minimum-weight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result
Limits of dense graph sequences
- J. Combin. Theory Ser. B
"... We show that if a sequence of dense graphs Gn has the property that for every fixed graph F, the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a symmetric measurable function W: [0,1] 2 → [0, 1]. This limit object determines all the limits of subgraph ..."
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Cited by 207 (18 self)
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We show that if a sequence of dense graphs Gn has the property that for every fixed graph F, the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a symmetric measurable function W: [0,1] 2 → [0, 1]. This limit object determines all the limits of subgraph
Approximating the permanent
- SIAM J. Computing
, 1989
"... Abstract. A randomised approximation scheme for the permanent of a 0-1 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the ..."
Abstract
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Cited by 345 (26 self)
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in the graph. For a wide class of 0-1 matrices the approximation scheme is fully-polynomial, i.e., runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output. This class includes all dense matrices (those that contain sufficiently many l’s) and almost all sparse
Performance-Effective and Low-Complexity Task Scheduling for Heterogeneous Computing
- IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2002
"... Efficient application scheduling is critical for achieving high performance in heterogeneous computing environments. The application scheduling problem has been shown to be NP-complete in general cases as well as in several restricted cases. Because of its key importance, this problem has been exte ..."
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Cited by 255 (0 self)
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with the related work, a parametric graph generator was designed to generate weighted directed acyclic graphs with various characteristics. The comparison study, based on both randomly generated graphs and the graphs of some real applications, shows that our scheduling algorithms significantly surpass previous
Computing communities in large networks using random walks
- J. of Graph Alg. and App. bf
, 2004
"... Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advan ..."
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Cited by 226 (3 self)
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Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important
Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
, 2001
"... This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift-invariant spaces. It is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift-invariant spaces by bringing togeth ..."
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Cited by 218 (13 self)
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of shift-invariant spaces. (b) The general theory works in arbitrary dimension and for a broad class of generators. (c) The reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms. These algorithms converge geometrically and are robust
ON NOWHERE DENSE GRAPHS
"... A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and rec ..."
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Cited by 7 (0 self)
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of nowhere dense graphs are quasi wide. This not only strictly generalizes the previous results and solves several open problems but it also provides new proofs. It appears that bounded expansion and nowhere dense classes are perhaps a proper setting for investigation of wide-type classes as in several
Fast random walk with restart and its applications
- In ICDM ’06: Proceedings of the 6th IEEE International Conference on Data Mining
, 2006
"... How closely related are two nodes in a graph? How to compute this score quickly, on huge, disk-resident, real graphs? Random walk with restart (RWR) provides a good relevance score between two nodes in a weighted graph, and it has been successfully used in numerous settings, like automatic captionin ..."
Abstract
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Cited by 179 (19 self)
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How closely related are two nodes in a graph? How to compute this score quickly, on huge, disk-resident, real graphs? Random walk with restart (RWR) provides a good relevance score between two nodes in a weighted graph, and it has been successfully used in numerous settings, like automatic
Results 1 - 10
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582
