Data Mining Practical Machine Learning Tools and Techniques

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Sphere Packings, Lattices and Groups

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

/pdf/introduction-to-random-graphs-3cfvwg09nu.pdf

Introduction to random graphs

Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches.- Connections in Networks: Hardness of Feasibility Versus Optimality.- Modeling the Regular Constraint with Integer Programming.- Hybrid Local Search for Constrained Financial Portfolio Selection Problems.- The "Not-Too-Heavy Spanning Tree" Constraint.- Eliminating Redundant Clauses in SAT Instances.- Cost-Bounded Binary Decision Diagrams for 0-1 Programming.- YIELDS: A Yet Improved Limited Discrepancy Search for CSPs.- A Global Constraint for Total Weighted Completion Time.- Computing Tight Time Windows for RCPSPWET with the Primal-Dual Method.- Necessary Condition for Path Partitioning Constraints.- A Constraint Programming Approach to the Hospitals / Residents Problem.- Best-First AND/OR Search for 0/1 Integer Programming.- A Position-Based Propagator for the Open-Shop Problem.- Directional Interchangeability for Enhancing CSP Solving.- A Continuous Multi-resources cumulative Constraint with Positive-Negative Resource Consumption-Production.- Replenishment Planning for Stochastic Inventory Systems with Shortage Cost.- Preprocessing Expression-Based Constraint Satisfaction Problems for Stochastic Local Search.- The Deviation Constraint.- The Linear Programming Polytope of Binary Constraint Problems with Bounded Tree-Width.- On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint.- Solving a Stochastic Queueing Control Problem with Constraint Programming.- Constrained Clustering Via Concavity Cuts.- Bender's Cuts Guided Large Neighborhood Search for the Traveling Umpire Problem.- A Large Neighborhood Search Heuristic for Graph Coloring.- Generalizations of the Global Cardinality Constraint for Hierarchical Resources.- A Column Generation Based Destructive Lower Bound for Resource Constrained Project Scheduling Problems.

Integration of AI and OR techniques in constraint programming for combinatorial optimization problems : 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007 : proceedings

We provide the first analytical results for the connectivity of dynamic random geometric graphs --- a model of mobile wireless networks in which vertices move in random directions, and an edge exists between two vertices if their Euclidean distance is below a given value. We provide precise asymptotic results for the expected length of the connectivity and disconnectivity periods of the network. We believe the formal tools developed in this work could be of use in more concrete settings, in the same manner as the development of connectivity threshold for static random geometric graphs has affected a lot of research done on ad hoc networks. In the process of proving results for the dynamic case we also obtain new asymptotically precise bounds for the probability of the existence of a component of fixed size l, l ≥ 2, for the static case.

https://www.cs.upc.edu/~diaz/papersd/SODAfinal.pdf

On the connectivity of dynamic random geometric graphs

On the satisfiability threshold of formulas with three literals per clause

We provide the first rigorous analytical results for the connectivity of dynamic random geometric graphs - a model for mobile wireless networks in which vertices move in random directions in the unit torus. The model presented here follows the one described. We provide precise asymptotic results for the expected length of the connectivity and disconnectivity periods of the network. We believe that the formal tools developed in this work could be extended to be used in more concrete settings and in more realistic models, in the same manner as the development of the connectivity threshold for static random geometric graphs has affected a lot of research done on ad hoc networks.

Large Connectivity for Dynamic Random Geometric Graphs

We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an m-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when m scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.

/pdf/dimensionality-of-social-networks-using-motifs-and-543dn61tsi.pdf

Dimensionality of Social Networks Using Motifs and Eigenvalues

The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the metric dimension of the random graph $G(n,p)$ for a wide range of probabilities $p=p(n)$.

/pdf/metric-dimension-for-random-graphs-42rxiayy94.pdf

Dieter Mitsche

Papers

On the connectivity of dynamic random geometric graphs

On the satisfiability threshold of formulas with three literals per clause

Large Connectivity for Dynamic Random Geometric Graphs

Dimensionality of Social Networks Using Motifs and Eigenvalues

Metric Dimension for Random Graphs