M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004. Home/Search Document Details and Download
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Locality, Hierarchy, and Bidirectionality in the Web - Eiron, Mccurley (2003) (Correct)
.... host in the dataset is shown in Figure 1(a) From 2 the fact that the log log plot for pages per host appears more quadratic than linear, we believe that this distribution is not a simple power law, but may instead be best described by a lognormal distribution or a double Pareto distrbution(see [13]) It should be noted however, that our crawling strategy, as well as the proliferation of aliases for hosts on the web, mean that this data is only approximate. Moving down the hierarchy, to the directory structure within hosts, one might wonder how the shapes of directory trees of web servers ....
M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1, 2003. to appear.
A General Model of Web Graphs - Cooper, Frieze (2003) (15 citations) (Correct)
....tail. One method of producing graph processes with a power law degree sequence is to introduce an element of preferential attachment (or copying) into the way that a new vertex attaches its edges to the existing graph. There is a long history of such models, outlined in the survey by Mitzenmacher [23]. We will use the preferential attachment model to generate our random graph. The preferential attachment random graph has been the subject of recently revived interest. It dates back to Yule [27] and Simon [25] It was proposed as a model for the web by Barab asi and Albert [2] and their ....
, M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions, to appear.
Modeling Query-Based Access to Text Databases - Agichtein, Ipeirotis, Gravano (2003) (2 citations) (Correct)
....of the reachability graph constructed for Task 2, for MaxResults equal to 1 and 10, respectively. The outdegree distribution follows a power law form for a large part of the distribution. We can model the distribution more accurately using extensions of the pure power law model (e.g. see [9]) but a full discussion of other candidate distributions is beyond the scope of this paper. For MaxResults=1 and 10 we have just one connected component, which includes all the tokens of the reachability graph. We conjecture that these observations will hold for the reachability graphs ....
M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. In First Workshop on Algorithms and Models for the Web-Graph, 2001.
Power-Laws and the AS-level Internet Topology - Siganos, Faloutsos.. (2003) (1 citation) (Correct)
.... [34] automobile networks [19] the size and location of earthquakes, stock price uctuations [6] the web of human sexual contacts [17] biological cellular networks [25] the scienti c citation network [50] More details about the historical aspects of power laws can be found by Mitzenmacher [38] and an extensive presentation of power laws in many diverse elds in Reka [3] Network analysis using power laws. More recently, powerlaws have been observed in communication networks. First, power laws have been observed in network trac [56] 30] 46] 13] In addition, the topology of the World ....
M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Allerton, 2001.
High Degree Vertices and Eigenvalues in the Preferential.. - Fenner, Flaxman (2003) (1 citation) (Correct)
....the development of various alternative models for random graphs. One approach to remedy this situation is to study graphs with a prescribed degree sequence (or prescribed expected degree sequence) This is proposed as a model for the web graph by Aiello, Chung, and Lu in [ACL00] Mihail and Papadimitriou also use this model [MP] in their study of large eigenvalues, which is extended by Chung, Lu, and Vu in [CLV] An alternative approach, which we will follow in this paper, is to sample graphs via some generative procedure which yields a power law distribution. There is a long history of such ....
....their study of large eigenvalues, which is extended by Chung, Lu, and Vu in [CLV] An alternative approach, which we will follow in this paper, is to sample graphs via some generative procedure which yields a power law distribution. There is a long history of such models, outlined in the survey by Mitzenmacher [Mit] We will use the preferential attachment model to generate our random graph. The preferential attachment random graph has been the subject of recently revived interest. It dates back to Yule [Yul25] and Simon [Sim55] It was proposed as a model for the web by Barab asi and Albert ....
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions.
Heuristically Optimized Trade-offs: A New Paradigm for Power.. - Fabrikant, al. (2002) (11 citations) (Correct)
....of other domains including, most notably, the degrees of the world wide web graph [9] they have been termed the 1 signature of human activity (even though they do occasionally arise in nature) 1 . There have been several attempts to explain power laws by so called generative models (see [12] for a technical survey) The vast majority of such models fall into one large category (with important di erences and formidable technical diculties, of course) that can be termed scale free growth or preferential attachment (or, more playfully, the rich get richer ) That is, if the growth of ....
M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Manuscript.
A Brief History of Generative Models for Power Law and.. - Mitzenmacher (22 citations) Self-citation (Mitzenmacher) (Correct)
....This paper represents an attempt Supported in part by an Alfred P. Sloan Research Fellowship and NSF grant CCR 9983832. Harvard University, Division of Engineering and Applied Sciences, 33 Oxford St. Cambridge, MA 02138. michaelm eecs.harvard.edu. A preliminary version of this work appeared as [64]. I apologize for leaving out countless further examples. I elaborate on this speci c model in another paper [63] to disseminate what I have found, focusing speci cally on the models of processes that generate these distributions. Perhaps the most interesting discovery is that much of ....
M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. In Proceedings of the Thirty-Ninth Annual Allerton Conference on Communication, Control, and Computing, pages 182-191, 2001.
Graphs over Time: Densification Laws, Shrinking.. - Leskovec, Kleinberg, .. (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004.
Heuristically Optimized Trade-o s: - New Paradigm For (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Manuscript.
Interpolating Between Types and Tokens - Estimating Power-Law Generators (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2):226--251, 2003.
The Shape of Production Functions and the Direction of Technical.. - Jones (2005) (Correct)
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Mitzenmacher, Michael, "A Brief History of Generative Models for Power Law and Lognormal Distributions," Internet Mathematics, I (2003), 226--251.
Graphs over Time: Densification Laws, Shrinking - Diameters And Possible (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004.
Graphs over Time: Densification Laws, Shrinking - Diameters And Possible (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004.
Laws of Graph Evolution: Densification and Shrinking.. - Leskovec, Kleinberg.. (2006) (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004.
Graphs over Time: Densification Laws, Shrinking - Diameters And Possible (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004.
Their share: diversity and disparity in IP traffic - Broido, Hyun, Gao, claffy (2004) (1 citation) (Correct)
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Mitzenmacher, M.: A brief history of generative models for power law and lognormal distributions. In: Internet Mathematics. (2003)
The essence of P2P: A reference architecture for overlay.. - Karl Aberer Luc (2005) (Correct)
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M. Mitzenmacher. A Brief History of Generative Models for Power Law and Lognormal Distributions. Draft manuscript. http://www.eecs.harvard.edu/ # michaelm/postscripts/ tempim1.ps, 2005.
Graphs over Time: Densification Laws, Shrinking.. - Leskovec, Kleinberg, .. (2005) (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions, 2004.
Reducing Large Internet Topologies - For Faster Simulations (2005) (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2), 2004.
Adversarial Deletion in a Scale Free Random Graph Process - Flaxman, Frieze, Vera (2004) (1 citation) (Correct)
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M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions,
A First-Principles Approach to Understanding the.. - Li, Alderson.. (2004) (7 citations) (Correct)
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M. Mitzenmacher. A Brief History of Generative Models for Power Law and Lognormal Distributions, Internet Mathematics. To appear. (2003)
A Survey of Models of the Web Graph - Bonato (Correct)
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M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions, Internet Mathematics 1 (2003) 226-251.
A Geometric Preferential Attachment Model Of Networks - Flaxman, Frieze, Vera (2004) (Correct)
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M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions,
Their share: diversity and disparity in IP traffic - Broido, Hyun, Gao, claffy (2004) (1 citation) (Correct)
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Mitzenmacher, M.: A brief history of generative models for power law and lognormal distributions. In: Internet Mathematics. (2003)
Random Deletion In A Scale Free Random Graph Process - Cooper, Frieze, Vera (2004) (2 citations) (Correct)
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M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. In Proc. of the 39th Annual Allerton Conf. on Communication, Control, and Computing, pages 182--191, 2001.
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