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-1-1Graph Theory Lessons
https://www.merlot.org/merlot/viewMaterial.htm?id=84776
<p>The applets contain topics typically found in undergraduate graph theory and discrete structures classes like null graphs, the handshaking lemma, isomorphism, complete graphs, subgraphs, regular graphs, platonic graphs, adjacency matrices, graph coloring, bipartite graphs, simple circuits, Euler and Hamilton circuits, trees, unions and sums of graphs, complements of graphs, line graphs, spanning trees, plane graphs, shortest paths, minimal spanning trees. The applet utilizes Petersen software written by the author. Peterson can draw, edit and manipulate simple graphs, examine properties of the graphs, and demonstrate them using computer animation.</p>Sat, 24 Sep 2005 07:00:00 GMTDr. Christopher P. Mawata University of Tennessee at ChattanoogaDiscrete Math Resources
https://www.merlot.org/merlot/viewMaterial.htm?id=363275
<p>This site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley and Winston Crawley. Requires Adobe Flash player.</p>Wed, 28 Jan 2009 03:07:46 GMTDoug Ensley Shippensburg UniversityGraph Theory Tutorials
https://www.merlot.org/merlot/viewMaterial.htm?id=86754
This is a series of short interactive tutorials introducing the basic concepts of graph theory. There is not a great deal of theory here, but enough will be taught to wet your appetite for more!Fri, 02 Jun 2006 07:00:00 GMTChris K. Caldwell University of Tennessee at MartinInteger Optimization and the Network Models
https://www.merlot.org/merlot/viewMaterial.htm?id=80563
It covers integer and network optimization with numerical examples and applicationsSun, 15 Feb 2004 08:00:00 GMTBarbra Bied Sperling CSU, Office of the ChancellorPrims Algorithm
https://www.merlot.org/merlot/viewMaterial.htm?id=74247
Interacive illustration of Prims algorithm.Mon, 07 Apr 1997 07:00:00 GMTDrossos NikolaosApplied Discrete Structures
https://www.merlot.org/merlot/viewMaterial.htm?id=740675
<p><strong>Applied Discrete Structures</strong> by <a href="http://faculty.uml.edu/math/faculty/doerr.htm" target="_new">Al Doerr</a> and <a href="http://faculty.uml.edu/klevasseur/" target="_new">Ken Levasseur</a> is a <em>free</em> open content textbook in discrete mathematics. Originally published in 1984 & 1989 by Pearson, the book has been updated to include references to Mathematica and Sage, the open source computer algebra system. </p><p><strong>Contents:</strong></p><p>Front Matter: Contents and Introduction</p><p><span>Chapter 1: Set Theory I</span><span> </span></p><p><span>Chapter 2: Combinatorics</span><span> </span></p><p><span>Chapter 3: Logic</span><span> </span></p><p><span>Chapter 4: More on Sets</span><span> </span></p><p><span>Chapter 5: Introduction to Matrix Algebra</span><span> </span></p><p><span>Chapter 6: Relations and Graphs</span><span> </span></p><p><span>Chapter 7: Functions</span><span> </span></p><p><span>Chapter 8: Recursion and Recurrence Relations</span><span> </span></p><p><span>Chapter 9: Graph Theory</span><span> </span></p><p><span>Chapter 10: Trees</span><span> </span></p><p><span>Chapter 11: Algebraic Systems</span><span> </span></p><p><span>Chapter 12: More Matrix Algebra</span><span> </span></p><p><span>Chapter 13: Boolean Algebra</span><span> </span></p><p><span>Chapter 14: Monoids and Automata</span><span> </span></p><p><span>Chapter 15: Group Theory and Applications</span><span> </span></p><p><span>Chapter 16: An Introduction to Rings and Fields</span><span> </span></p><p><span>Solutions to Odd-Numbered Exercises</span><span> </span></p>Thu, 14 Mar 2013 16:17:19 GMTKen Levasseur; Alan Doerr UMass LowellGraph Matching Algorithms
https://www.merlot.org/merlot/viewMaterial.htm?id=974114
This video was recorded at Machine Learning Summer School (MLSS), Canberra 2005. Graph matching plays a key role in many areas of computing from computer vision to networks where there is a need to determine correspondences between the components (vertices and edges) of two attributed structures. In recent years three new approaches to graph matching have emerged as replacements to more traditional heuristic methods. These new methods are: * Least squares - where the optimal correspondence in determined in terms of deriving the best fitting permutation matrix between sets. * Spectral methods - where optimal correspondences are derived via subspace projections in the graph eigenspaces. * Graphical models - where algorithms such as the junction tree algorithm are used to infer the optimal labeling of the nodes of one graph in terms of the other and that satisfy similarity constraints between vertices and edges. In this lecture we review and compare these methods and demonstrate examples where this applies to point set and line matching.Tue, 10 Feb 2015 21:28:34 GMTTerry Caelli NICTA, Australia's ICT Research Centre of Excellence'Lies, Damn Lies, and Statistics': A Critical Assessment of Preferential Attachment-type Network Models of the Internet
https://www.merlot.org/merlot/viewMaterial.htm?id=940895
This video was recorded at 4th European Conference on Complex Systems. Basic Question: Do the available Internet-related connectivity measurements and their analysis support the sort of claims that can be found in the existing complex networks literature? Key Issues: What about data hygiene? What about statistical rigor? What about model validation? Author discusses some of the main problems and challenges associated with measuring, inferring, and modeling various types of Internet-related connectivity structures. To this end, he uses some known examples to illustrate the need to understand the process by which Internet connectivity measurements are obtained, explore the sensitivity of inferred graph properties to known ambiguities in the data, be more critical with respect to the dominant, preferential attachmenttype network modeling paradigm, and be more serious/ambitious when it comes to model validation. Ignoring any of these issues is bound to produce results that are best described by the well-known aphorism "lies, damned lies, and statistics."Mon, 09 Feb 2015 05:11:25 GMTWalter Willinger AT&T Labs, Inc. - ResearchA Century of Graph Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=944078
This video was recorded at Predavanja, seminarji in srečanja na Fakulteti za matematiko in fiziko. Graph theory has changed completely from the late-19th century to the late 20th century, from a collection of mainly recreational problems to a well-developed mainstream area of mathematics. In this talk I outline its development over this period, both chronologically and thematically.Mon, 09 Feb 2015 05:38:06 GMTRobin J. Wilson Department of Mathematics and Statistics, Open University (OU)A Polynomial-time Metric for Outerplanar Graphs (Extended Abstract)
https://www.merlot.org/merlot/viewMaterial.htm?id=973621
This video was recorded at 5th International Workshop on Mining and Learning with Graphs (MLG), Firenze 2007. In the chemoinformatics context, graphs have become very popular for the representation of molecules. However, a lot of algorithms handling graphs are computationally very expensive. In this paper we focus on outerplanar graphs, a class of graphs that is able to represent the majority of molecules. We define a metric on outerplanar graphs that is based on finding a maximum common subgraph and we present an algorithm that runs in polynomial time. Having an efficiently computable metric on molecules can improve the virtual screening of molecular databases significantly.Tue, 10 Feb 2015 21:24:05 GMTLeander Schietgat Department of Computer Science, KU LeuvenA Quadratic Programming Approach to the Graph Edit Distance Problem
https://www.merlot.org/merlot/viewMaterial.htm?id=944442
This video was recorded at 6th IAPR - TC-15 Workshop on Graph-based Representations in Pattern Recognition (GbR), Alicante 2007. In this paper we propose a quadratic programming approach to computing the edit distance of graphs. Whereas the standard edit distance is defined with respect to a minimum-cost edit path between graphs, we introduce the notion of fuzzy edit paths between graphs and provide a quadratic programming formulation for the minimization of fuzzy edit costs. Experiments on real-world graph data demonstrate that our proposed method is able to outperform the standard edit distance method in terms of recognition accuracy on two out of three data sets.Mon, 09 Feb 2015 05:41:28 GMTHorst Bunke University of BernAn Information Theoretic Approach to Learning Generative Graph Prototypes
https://www.merlot.org/merlot/viewMaterial.htm?id=979571
This video was recorded at 1st International Workshop on Similarity-Based Pattern Analysis and Recognition. We present a method for constructing a generative model for sets of graphs by adopting a minimum description length approach. The method is posed in terms of learning a generative supergraph model from which the new samples can be obtained by an appropriate sampling mechanism. We commence by constructing a probability distribution for the occurrence of nodes and edges over the supergraph. We encode the complexity of the supergraph using the von-Neumann entropy. A variant of EM algorithm is developed to minimize the description length criterion in which the node correspondences between the sample graphs and the supergraph are treated as missing data.The maximization step involves updating both the node correspondence information and the structure of supergraph using graduated assignment. In the experimental part, we demonstrate the practical utility of our proposed algorithm and show that our generative model gives good graph classification results. Besides, we show how to perform graph clustering with Jensen-Shannon kernel and generate new sample graphs.Tue, 10 Feb 2015 22:14:59 GMTEdwin Hancock Department of Computer Science, University of YorkApproximate Graph Products
https://www.merlot.org/merlot/viewMaterial.htm?id=939378
This video was recorded at Complex Objects Visualization Workshop, Koper 2005. Products of graphs allow a rather compressed coding from the data structure point of view and often transparent graphical representations. Graphs that differ little from products in the sense that addition or deletion of a small number of edges turns them into a product offer similar advantages.Mon, 09 Feb 2015 04:59:39 GMTWilfried Imrich University of LeobenBasic and Advanced Operations on Graphs
https://www.merlot.org/merlot/viewMaterial.htm?id=944032
This video was recorded at Discrete Mathematics 2 + Configurations Lectures.Mon, 09 Feb 2015 05:37:39 GMTTomaž Pisanski Inštitut za matematiko, fiziko in mehaniko (IMFM)Bilateral Symmetry Detection via Symmetry-Growing
https://www.merlot.org/merlot/viewMaterial.htm?id=937075
This video was recorded at British Machine Vision Conference (BMVC), London 2009. The British Machine Vision Conference is the main UK conference on machine vision and the related areas. Organized by the British Machine Vision Association, the 20'th BMVC was held in London and jointly run by Queen Mary and UCL. The conference homepage can be found at British Machine Vision Conference 2009Mon, 09 Feb 2015 04:37:39 GMTMinsu Cho Computer Vision Lab, Seoul National UniversityBipartite Graph Matching for Computing the Edit Distance of Graphs
https://www.merlot.org/merlot/viewMaterial.htm?id=944490
This video was recorded at 6th IAPR - TC-15 Workshop on Graph-based Representations in Pattern Recognition (GbR), Alicante 2007. In the field of structural pattern recognition graphs constitute a very common and powerful way of representing patterns. In contrast to string representations, graphs allow us to describe relational information in the patterns under consideration. One of the main drawbacks of graph representations is that the computation of standard graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for rather small graphs only. One of the most flexible error-tolerant graph similarity measures is based on graph edit distance. In this paper we propose an approach for the efficient compuation of edit distance based on bipartite graph matching by means of Munkres' algorithm, sometimes referred to as the Hungarian algorithm. Our proposed algorithm runs in polynomial time, but provides only suboptimal edit distance results. The reason for its suboptimality is that implied edge operations are not considered during the process of finding the optimal node assignment. In experiments on semi-artificial and real data we demonstrate the speedup of our proposed method over a traditional tree search based algorithm for graph edit distance computation. Also we show that classification accuracy remains nearly unaffected.Mon, 09 Feb 2015 05:41:56 GMTKaspar Riesen University of BernCalculus on Graphs
https://www.merlot.org/merlot/viewMaterial.htm?id=939328
This video was recorded at Workshop on Function Prediction in Complex Networks, Kavli Royal Society Centre, Chicheley Hall 2012. The workshop was funded by the Royal Society under the the Research Fellows International Scientific Seminars scheme, and the PASCAL2 network provided funding to cover the filming. The aim of the meeting was to bring together researchers from complex networks, and those working in machine learning and graph theory. The goal was to identify current challenges in complex networks analysis and identify possible methodologies for addressing them. The meeting was composed of four sessions: methods for measuring and characterising complex network structure. dynamic processes on complex networks. complex network function prediction. future directions, collaboration and networking. The presentations were not intended to be lectures focused on specific research results. Instead they were expected to summarize state-of-the-art or accepted wisdom, challenge it and pose a provocative agenda for the discussions. We thank Sir Peter Knight and the staff at the Royal Society Kavli Centre for providing a conducive and enjoyable environment for the meeting.Mon, 09 Feb 2015 04:59:11 GMTJoel Friedman Department of Mathematics, University of British ColumbiaCelestial and Polycycle Graphs
https://www.merlot.org/merlot/viewMaterial.htm?id=944054
This video was recorded at Discrete Mathematics 2 + Configurations Lectures.Mon, 09 Feb 2015 05:37:51 GMTTomaž Pisanski Inštitut za matematiko, fiziko in mehaniko (IMFM)Chinese Rings and Hanoi Tower Graphs
https://www.merlot.org/merlot/viewMaterial.htm?id=936606
This video was recorded at VideoLectures.NET - Single Lectures Series. The Single Lectures Series is an attempt of the VideoLectures.NET team to place on one page all the talks that were filmed but do not relate to any particular organized event, workshop, conference or course. Most of these talks were filmed at the University of Ljubljana, the Jozef Stefan institute and different cities in Slovenia. Some of them are also upload attempts of faculty from all over the world to post a talk on our site. We will continue to grow and expand this section as much as possible by sending our crew to film one off single talks that caught our attention.Mon, 09 Feb 2015 04:33:48 GMTAndreas M. Hinz University of MunichChordal Sparsity in Semidefinite Programming and Machine Learning
https://www.merlot.org/merlot/viewMaterial.htm?id=975919
This video was recorded at NIPS Workshops, Whistler 2009. Chordal graphs play a fundamental role in algorithms for sparse matrix factorization, graphical models, and matrix completion problems. In matrix optimization chordal sparsity patterns can be exploited in fast algorithms for evaluating the logarithmic barrier function of the cone of positive definite matrices with a given sparsity pattern and of the corresponding dual cone. We will give a survey of chordal sparse matrix methods and discuss two applications in more detail: linear optimization with sparse matrix cone constraints, and the approximate solution of dense quadratic programs arising in support vector machine training.Tue, 10 Feb 2015 21:45:03 GMTLieven Vandenberghe Electrical Engineering Department, University of California, Los Angeles, UCLAClassification in Graphs using Discriminative Random Walks
https://www.merlot.org/merlot/viewMaterial.htm?id=973633
This video was recorded at 6th International Workshop on Mining and Learning with Graphs (MLG), Helsinki 2008. This paper describes a novel technique, called D-walks, to tackle semi-supervised classification problems in large graphs. We introduce here a betweenness measure based on passage times during random walks of bounded lengths in the input graph. The class of unlabeled nodes is predicted by maximizing the betweenness with labeled nodes. This approach can deal with directed or undirected graphs with a linear time complexity with respect to the number of edges, the maximum walk length considered and the number of classes. Preliminary experiments on the CORA database show that D-walks outperforms NetKit (Macskassy & Provost, 2007) as well as Zhou et al's algorithm (Zhou et al., 2005), both in classification rate and computing time.Tue, 10 Feb 2015 21:24:11 GMTJerome Callut University of LouvainCombining near-optimal feature selection with gSpan
https://www.merlot.org/merlot/viewMaterial.htm?id=973653
This video was recorded at 6th International Workshop on Mining and Learning with Graphs (MLG), Helsinki 2008. Graph classification is an increasingly important step in numerous application domains, such as function prediction of molecules and proteins, computerized scene analysis, and anomaly detection in program flows. Among the various approaches proposed in the literature, graph classification based on frequent subgraphs is a popular branch: Graphs are represented as (usually binary) vectors, with components indicating whether a graph contains a particular subgraph that is frequent across the dataset. On large graphs, however, one faces the enormous problem that the number of these frequent subgraphs may grow exponentially with the size of the graphs, but only few of them possess enough discriminative power to make them useful for graph classification. Efficient and discriminative feature selection among frequent subgraphs is hence a key challenge for graph mining. In this article, we propose an approach to feature selection on frequent subgraphs, called CORK, that combines two central advantages. First, it optimizes a sub modular quality criterion, which means that we can yield a near-optimal solution using greedy feature selection. Second, our sub modular quality function criterion can be integrated into gSpan, the state-of-the-art tool for frequent subgraph mining, and help to prune the search space for discriminative frequent subgraphs even during frequent subgraph mining.Tue, 10 Feb 2015 21:24:21 GMTMarisa Thoma University of MunichCommunicability in Complex Networks
https://www.merlot.org/merlot/viewMaterial.htm?id=939326
This video was recorded at Workshop on Function Prediction in Complex Networks, Kavli Royal Society Centre, Chicheley Hall 2012. The workshop was funded by the Royal Society under the the Research Fellows International Scientific Seminars scheme, and the PASCAL2 network provided funding to cover the filming. The aim of the meeting was to bring together researchers from complex networks, and those working in machine learning and graph theory. The goal was to identify current challenges in complex networks analysis and identify possible methodologies for addressing them. The meeting was composed of four sessions: methods for measuring and characterising complex network structure. dynamic processes on complex networks. complex network function prediction. future directions, collaboration and networking. The presentations were not intended to be lectures focused on specific research results. Instead they were expected to summarize state-of-the-art or accepted wisdom, challenge it and pose a provocative agenda for the discussions. We thank Sir Peter Knight and the staff at the Royal Society Kavli Centre for providing a conducive and enjoyable environment for the meeting.Mon, 09 Feb 2015 04:59:10 GMTErnesto Estrada Institute of Complex Systems at Strathclyde, University of StrathclydeComplex Networks: Overview and Perspectives
https://www.merlot.org/merlot/viewMaterial.htm?id=939318
This video was recorded at Workshop on Function Prediction in Complex Networks, Kavli Royal Society Centre, Chicheley Hall 2012. The workshop was funded by the Royal Society under the the Research Fellows International Scientific Seminars scheme, and the PASCAL2 network provided funding to cover the filming. The aim of the meeting was to bring together researchers from complex networks, and those working in machine learning and graph theory. The goal was to identify current challenges in complex networks analysis and identify possible methodologies for addressing them. The meeting was composed of four sessions: methods for measuring and characterising complex network structure. dynamic processes on complex networks. complex network function prediction. future directions, collaboration and networking. The presentations were not intended to be lectures focused on specific research results. Instead they were expected to summarize state-of-the-art or accepted wisdom, challenge it and pose a provocative agenda for the discussions. We thank Sir Peter Knight and the staff at the Royal Society Kavli Centre for providing a conducive and enjoyable environment for the meeting.Mon, 09 Feb 2015 04:59:05 GMTMarc Barthélémy French Alternative Energies and Atomic Energy Commission (CEA)