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On the nonplanarity of a random subgraph
, 2012
"... Let G be a finite graph with minimum degree r. Form a random subgraph Gp of G by taking each edge of G into Gp independently and with probability p. We prove that for any constant ǫ> 0, if p = 1+ǫ r, then Gp is nonplanar with probability approaching 1 as r grows. This generalizes classical resul ..."
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Cited by 3 (3 self)
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Let G be a finite graph with minimum degree r. Form a random subgraph Gp of G by taking each edge of G into Gp independently and with probability p. We prove that for any constant ǫ> 0, if p = 1+ǫ r, then Gp is nonplanar with probability approaching 1 as r grows. This generalizes classical
Frequent Subgraph Discovery
, 2001
"... Over the years, frequent itemset discovery algorithms have been used to solve various interesting problems. As data mining techniques are being increasingly applied to nontraditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of th ..."
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Cited by 407 (14 self)
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of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the database objects. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a
Inducing Features of Random Fields
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the ..."
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Cited by 664 (14 self)
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We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing
Random key predistribution schemes for sensor networks
 IN PROCEEDINGS OF THE 2003 IEEE SYMPOSIUM ON SECURITY AND PRIVACY
, 2003
"... Key establishment in sensor networks is a challenging problem because asymmetric key cryptosystems are unsuitable for use in resource constrained sensor nodes, and also because the nodes could be physically compromised by an adversary. We present three new mechanisms for key establishment using the ..."
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Cited by 813 (14 self)
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the framework of predistributing a random set of keys to each node. First, in the qcomposite keys scheme, we trade off the unlikeliness of a largescale network attack in order to significantly strengthen random key predistribution’s strength against smallerscale attacks. Second, in the multipath
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
An algorithm for subgraph isomorphism
 JOURNAL OF THE ACM
, 1976
"... Subgraph isomorphism can be determined by means of a bruteforce treesearch enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph is ..."
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Cited by 341 (1 self)
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Subgraph isomorphism can be determined by means of a bruteforce treesearch enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph
Results 1  10
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145,170