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1,271
Depth first search and linear graph algorithms
 SIAM JOURNAL ON COMPUTING
, 1972
"... The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect ..."
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Cited by 1406 (19 self)
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The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components
Measurement and Analysis of Online Social Networks
 In Proceedings of the 5th ACM/USENIX Internet Measurement Conference (IMC’07
, 2007
"... Online social networking sites like Orkut, YouTube, and Flickr are among the most popular sites on the Internet. Users of these sites form a social network, which provides a powerful means of sharing, organizing, and finding content and contacts. The popularity of these sites provides an opportunity ..."
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Cited by 698 (14 self)
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contain a densely connected core of highdegree nodes; and that this core links small groups of strongly clustered, lowdegree nodes at the fringes of the network. Finally, we discuss the implications of these structural properties for the design of social network based systems.
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 ..."
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Cited by 414 (21 self)
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of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight 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
The Average Distance in a Random Graph with Given Expected Degrees
"... Random graph theory is used to examine the “smallworld phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d whe ..."
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Cited by 289 (13 self)
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Random graph theory is used to examine the “smallworld phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d
Bounding the strong chromatic index of dense random graphs
 Discrete Math
, 2004
"... For a graph G, a strong edge coloring of G is an edge coloring in which every color class is an induced matching. The strong chromatic index of G, χs(G), is the smallest number of colors in a strong edge coloring of G. In [9], Z. Palka proved that if p = p(n) = Θ(n−1), then with high probability, ..."
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Cited by 2 (1 self)
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For a graph G, a strong edge coloring of G is an edge coloring in which every color class is an induced matching. The strong chromatic index of G, χs(G), is the smallest number of colors in a strong edge coloring of G. In [9], Z. Palka proved that if p = p(n) = Θ(n−1), then with high probability
Algorithms for dense graphs and networks on the random access computer
 ALGORITHMICA
, 1996
"... We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size L = f2 (log n) a maximal matching in an nvertex bipartite graph in time O (n 2 + n2"5/~.) = O (n2"5/log n), how to com ..."
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Cited by 28 (4 self)
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We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size L = f2 (log n) a maximal matching in an nvertex bipartite graph in time O (n 2 + n2"5/~.) = O (n2"5/log n), how
Implementation of a Portable Nested DataParallel Language
 Journal of Parallel and Distributed Computing
, 1994
"... This paper gives an overview of the implementation of Nesl, a portable nested dataparallel language. This language and its implementation are the first to fully support nested data structures as well as nested dataparallel function calls. These features allow the concise description of parallel alg ..."
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Cited by 205 (28 self)
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. It runs on the Connection Machine CM2, the Cray YMP C90, and serial machines. We compare initial benchmark results of Nesl with those of machinespecific code on these machines for three algorithms: leastsquares linefitting, median finding, and a sparsematrix vector product. These results show
STRONG APPROXIMATION IN RANDOM TOWERS OF GRAPHS
, 2009
"... The term strong approximation is used to describe phenomena where an arithmetic group as well as all of its Zariski dense subgroups have a large image in the congruence quotients. We exhibit analogues of such phenomena in a probabilistic, rather than arithmetic, setting. Let T be the binary rooted t ..."
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Cited by 1 (0 self)
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tree, Aut(T) its automorphism group. To a given mtuple a = {a1, a2,..., am} ∈ Aut(T) m we associate a tower of 2mregular Schreier graphs... → Xn → Xn−1 →... → X0. The vertices of Xn are the n th level of the tree and two such x, y ∈ Xn are connected by an edge if y = x ai or if x = y ai for some i
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 140 (11 self)
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algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
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