Computer graphics homework help
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The document outlines a course on graph theory, covering various types of graphs, their properties, and algorithmic techniques for solving graph problems. It includes practical applications in fields such as telecommunications and networking, and aims to equip students with skills for designing efficient algorithms. Additionally, it promotes assignment help and tutoring services offered by Global Web Tutors.
Computer graphics homework help
- 2. To paraphrase what Felix Klein said about curves,1 it is easy to dene a graph until you realize the countless number of exceptions. There are directed graphs, weighted graphs, multigraphs, simple graphs, and so on. Where do we begin?
- 3. Typical topics include: Introduction to graphs: undirected graphs, directed graphs, weighted graphs, graph representation and special classes of graphs (trees, planar graphs etc.). Applications of graphs (in telecommunications, networking etc.). Basic algorithmic techniques for graph problems: graph traversals (DFS and BFS), topological sorting, Eular tours. Further algorithmic problems on graphs: minimum spanning trees, shortest path problems, matching problems. Planar graphs and their properties. Eular's formula, planar separateor theorem and their algorithmic applications. Further optimization problems on graphs including graph colouring and graph questions in distributed systems. Discussing practical applications of graphs and efficient algorithms for such practical problems. Approximation algorithms and heuristic algorithms. Applications to searching in massive graphs (e.g. page ranking); use of structural properties and algebraic properties.
- 4. Learning Outcomes On completion of the module the student shoud be able to: understand the basics of graphs, directed graphs, weighted graphs and be able to relate them to practical examples. use effectively algorithmic techniques to study basic parameters and properties of graphs. design efficient algorithms for various optimisation problems on graphs. use effectively techniques from graph theory to approach practical problems in networking and communication.
- 8. Introduction Definitions and Examples Eulerian Graphs Hamiltonian Graphs Graph Connectivity Tree Graphs Graph Planarity Graph Embedding Graph Coloring
- 9. AGD -- LEDA-based library of C++ classes for graph drawing. aiSee -- graph drawing tool that supports a variety of layout methods. Graph Drawing Server -- Web-based graph drawing service. Graph Drawing Tools and Related Work Graphviz -- open source graph drawing software at AT&T. GDToolkit -- LEDA-based library of C++ classes for graph drawing. 3DCube -- tool for 3D graph drawing. Peterson -- software that can draw, edit and manipulate simple graphs, examine properties of the graphs, and demonstrate them using computer animation. Graph Theory Lessons -- A set of lessons (undergraduate level) that go with the software 'Petersen'.
- 10. Combinatorica Combinatorics, Probability, and Computing Discrete Applied Mathematics Discrete Mathematics Discussiones Mathematicae. Graph Theory Graphs and Combinatorics Graph Theory Journals Information Processing Letters Journal of Combinatorial Theory, Series A Journal of Combinatorial Theory, Series B Journal of Graph Theory Journal of Graph Algorithms and Applications Electronic Journal of Combinatorics European Journal of Combinatorics Theoretical Computer Science
- 11. Graphs are very basic objects in discrete mathematics, and are particularly useful in modeling a wide variety of problems. This course will have multiple objectives. First, we will study several basic concepts in graph theory, getting a broad introduction to the area and the different techniques used. Next, we will study the algorithmic aspects of various graph theoretic problems. The focus will be on understanding how structural results in graph theory are useful in designing both exact and approximation algorithm for various fundamental and practical optimization problems. We will also see how linear programming and semi-definite programming play a key role here, providing us with a glimpse of the rich area of combinatorial optimization. Towards the end of the course, we will study some more advanced (recent) results in the area. It will be interesting to see how the various techniques we studied come together to give these surprising new results.
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