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A Random Graph Model for Massive Graphs
, 2000
"... We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and loglog growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from the ..."
Abstract

Cited by 335 (26 self)
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We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and loglog growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model.
A Random Graph Model for Power Law Graphs
 Experimental Math
, 2000
"... We propose a random graph m del which is a special case of sparse random graphs with given degree sequences which satisfy a power law. Thism odel involves only asm all num ber of param eters, called logsize and loglog growth rate. These param eters capturesom e universal characteristics ofm assive ..."
Abstract

Cited by 73 (4 self)
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We propose a random graph m del which is a special case of sparse random graphs with given degree sequences which satisfy a power law. Thism odel involves only asm all num ber of param eters, called logsize and loglog growth rate. These param eters capturesom e universal characteristics ofm assive graphs. Furtherm re, from these paramfi ters, various properties of the graph can be derived. Forexam)(( for certain ranges of the paramJ?0CM we willcom?C7 the expected distribution of the sizes of the connectedcom onents which almJC surely occur with high probability. We will illustrate the consistency of our m del with the behavior of so m m ssive graphs derived from data in telecom unications. We will also discuss the threshold function, the giant com ponent, and the evolution of random graphs in thism del. 1
The Complexity of Learning with Queries
, 1994
"... We survey recent research concerning the qualitative complexity of Angluin 's model of learning with queries. In this model, there is a learner that tries to identify a target concept by means of queries to a teacher. Thus, the process can be naturally formulated as an oracle computation. Among the ..."
Abstract

Cited by 11 (1 self)
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We survey recent research concerning the qualitative complexity of Angluin 's model of learning with queries. In this model, there is a learner that tries to identify a target concept by means of queries to a teacher. Thus, the process can be naturally formulated as an oracle computation. Among the results we review there are: characterizations of the power of different learning protocols by complexity classes of oracle machines; relations between the complexity of learning and the complexity of computing advice functions for nonuniform classes; and combinatorial characterizations of the concept classes that are learnable in specific protocols. 1 Introduction This paper is a survey on recent results and ideas on the qualitative complexity of Angluin's model of learning with queries, also known as query learning or exact learning. This model is quickly becoming one of the most popular ones the computational learning community, receiving almost as much attention as more traditional mode...
The General Steiner TreeStar Problem
 INFORMATION PROCESSING LETTERS
, 2002
"... The Steiner tree problem is de ned as follows  given a graph G = (V; E) and a subset X V of terminals, compute a minimum cost tree that includes all nodes in X . Furthermore, it is reasonable to assume that the edge costs form a metric. This problem is NPhard and has been the study of many heuri ..."
Abstract

Cited by 11 (0 self)
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The Steiner tree problem is de ned as follows  given a graph G = (V; E) and a subset X V of terminals, compute a minimum cost tree that includes all nodes in X . Furthermore, it is reasonable to assume that the edge costs form a metric. This problem is NPhard and has been the study of many heuristics and algorithms. We study a generalization of this problem, where there is a \switch" cost in addition to the cost of the edges. Switches are placed at internal nodes of the tree (essentially, we may assume that all nonleaf nodes of the Steiner tree have a switch). The cost for placing a switch may vary from node to node. A restricted version of this problem, where the terminal set X cannot be connected to each other directly but only via the Steiner nodes V n X , is referred to as the Steiner TreeStar problem. The General Steiner TreeStar problem does not require the terminal set and Steiner node set to be disjoint. This generalized problem can be reduced to the node weighted Steiner tree problem, for which algorithms with performance guarantees of (ln n) are known. However, such approach does not make use of the fact that the edge costs form a metric. In this paper we derive approximation algorithms with small constant factors for this problem. We show two dierent polynomial time algorithms with approximation factors of 5.16 and 5.