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**11 - 16**of**16**### WWW Graphs Call Graphs Collaboration Graphs Gene Regulatory Graphs

"... A graph consists of two sets V and E.- V is the set of vertices (or nodes).- E is the set of edges, where each edge is a pair of vertices. ..."

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A graph consists of two sets V and E.- V is the set of vertices (or nodes).- E is the set of edges, where each edge is a pair of vertices.

### zur Erlangung des Grades eines

"... Symbolic dynamics and scattering theory for localized magnetic fields ..."

### Infinite Limits of Stochastic Graph Models

"... We present new generalized copying models for massive self-organizing networks such as the web graph, and analyze their limit behaviour. Our model is motivated by a desire to unify common design elements of the copying models of the web graph, and the partial duplication model for biological net ..."

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We present new generalized copying models for massive self-organizing networks such as the web graph, and analyze their limit behaviour. Our model is motivated by a desire to unify common design elements of the copying models of the web graph, and the partial duplication model for biological networks. In these models, new nodes copy (with some error) the link structure of existing nodes, and a certain number of random links may be added to the new node that can link to any of the existing nodes. In our new models, a function # parameterizes the number of random links, and thereby allows for the analysis of threshold behaviour.

### Scalable Computing for Power Law Graphs: . . .

"... In this paper we investigate the numerical and parallel performance of linear algebra algorithms when applied to power law data typical for information retrieval. In particular, we report on the behavior of parallel numerical algorithms applied to computing the PageRank vector for a 1.5 billion node ..."

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In this paper we investigate the numerical and parallel performance of linear algebra algorithms when applied to power law data typical for information retrieval. In particular, we report on the behavior of parallel numerical algorithms applied to computing the PageRank vector for a 1.5 billion node directed web graph. We also describe the details of our parallel implementation that was able to compute the PageRank vector for this web graph on a distributed memory 140 processor RLX cluster in under 6 minutes.

### On reversible cascades in scale-free and Erdős-Rényi random graphs

, 2010

"... ar ..."

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### Average-case analysis for combinatorial problems

, 2006

"... This thesis considers the average case analysis of algorithms, focusing primarily on NP-hard combinatorial optimization problems. It includes a catalog of distributions frequently used in average-case analysis and a collection of mathematical tools that have been useful in studying these distributio ..."

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This thesis considers the average case analysis of algorithms, focusing primarily on NP-hard combinatorial optimization problems. It includes a catalog of distributions frequently used in average-case analysis and a collection of mathematical tools that have been useful in studying these distributions. The bulk of the thesis consists of case-studies in average-case analysis of algorithms. Algorithms for 3-SAT, Subset Sum, Strong Connectivity, Stochastic Minimum Spanning Tree, and Uncapacitated Facility Location are analyzed on random instances.