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364,264
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 532 (48 self)
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increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification
On Compact Encoding of Pagenumber k Graphs
, 2001
"... this paper we show an informationtheoretic lower bound of kn o(kn) on the minimum number of bits to represent an unlabeled connected nnode graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn +2m+o(n) bits, that is 4kn +2n k ..."
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Cited by 8 (1 self)
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this paper we show an informationtheoretic lower bound of kn o(kn) on the minimum number of bits to represent an unlabeled connected nnode graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn +2m+o(n) bits, that is 4kn +2n k
Small InducedUniversal Graphs and Compact Implicit Graph Representations
 In Proc. 43’rd annual IEEE Symp. on Foundations of Computer Science
, 2002
"... We show that there exists a graph G with n 2 nodes, where any forest with n nodes is a nodeinduced subgraph of G. Furthermore, the result implies existence of a graph with n nodes that contains all nnode graphs of fixed arboricity k as nodeinduced subgraphs. We provide a lower bound ..."
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Cited by 18 (1 self)
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We show that there exists a graph G with n 2 nodes, where any forest with n nodes is a nodeinduced subgraph of G. Furthermore, the result implies existence of a graph with n nodes that contains all nnode graphs of fixed arboricity k as nodeinduced subgraphs. We provide a lower bound
Fusion, Propagation, and Structuring in Belief Networks
 ARTIFICIAL INTELLIGENCE
, 1986
"... Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to repre ..."
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Cited by 480 (8 self)
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Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used
A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 432 (3 self)
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and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log2N + 2E, and a message contains at most one edge weight plus log28N bits. The algorithm can be initiated spontaneously at any node or at any subset
Lower bounds for recognizing small cliques on CRCW PRAM’s
 Discrete Appl. Math
, 1990
"... We show that any CRCW PRAM which recognizes kcliques in nnode graphs in time T requires at least nn(k’r2) processors independent of its memory size. As a corollary we obtain essentially the same tradeoff for unbounded fanin circuits. We also demonstrate a similar but weaker tradeoff for the me ..."
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Cited by 6 (1 self)
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We show that any CRCW PRAM which recognizes kcliques in nnode graphs in time T requires at least nn(k’r2) processors independent of its memory size. As a corollary we obtain essentially the same tradeoff for unbounded fanin circuits. We also demonstrate a similar but weaker trade
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 147 (9 self)
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and Widmayer and finds applications in VLSI design. The group Steiner tree problem generalizes the set covering problem, and is therefore at least as had. We give a randomized O(log 3 n log k)approximation algorithm for the group Steiner tree problem on an nnode graph, where k is the number of groups
A Note on Implicit Representation of Graphs
, 2001
"... An implicit representation for a given family of graphs is a node labeling scheme of all the nnode graphs of the family by binary strings of length O(log n) such that adjacency between any two nodes can be decided from their labels only. In this note, we design a 3 log nbit labeling scheme for pla ..."
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An implicit representation for a given family of graphs is a node labeling scheme of all the nnode graphs of the family by binary strings of length O(log n) such that adjacency between any two nodes can be decided from their labels only. In this note, we design a 3 log nbit labeling scheme
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 350 (6 self)
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In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied
O (√log n) approximation to SPARSEST CUT can be found in Õ(n²) time
 FOCS 2004 SUBMISSION
, 2004
"... We show that the recent results for obtaining O ( √ log n)approximation to sparsest cut and balanced separator problems due to Arora, Rao, and Vazirani (2004) can be used to derive an Õ(n²) time approximation algorithm for an nnode graph. The previous best algorithm needed to solve a semidefinite ..."
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We show that the recent results for obtaining O ( √ log n)approximation to sparsest cut and balanced separator problems due to Arora, Rao, and Vazirani (2004) can be used to derive an Õ(n²) time approximation algorithm for an nnode graph. The previous best algorithm needed to solve a
Results 1  10
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