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Discrete Mathematics I Lectures Chapter 10

Discrete Mathematics I Lectures Chapter 10. Some material adapted from lecture notes provided by Dr. Chungsim Han and Dr. Sam Lomonaco. Dr. Adam Anthony Spring 2011. Section 10.1. Introduction to Graphs.

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Week 3: Minimum Spanning Trees

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Analysis of Algorithms CS 477/677

Analysis of Algorithms CS 477/677. Shortest Paths Instructor: George Bebis Chapter 24. Shortest Path Problems. How can we find the shortest route between two points on a road map? Model the problem as a graph problem: Road map is a weighted graph: vertices = cities

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A Novel Method for Signal Transduction Network Inference from Indirect Experimental Evidence Bhaskar DasGupta Department

A Novel Method for Signal Transduction Network Inference from Indirect Experimental Evidence Bhaskar DasGupta Department of Computer Science University of Illinois at Chicago Chicago, IL 60607-7053 dasgupta@cs.uic.edu. Acknowledgements

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Data Structures Lecture 14

Fall 2010. Data Structures Lecture 14. Fang Yu Department of Management Information Systems National Chengchi University. Graphs. Definition, Implementation and Traversal. Graphs. Formally speaking, a graph is a pair ( V, E ) , where V is a set of nodes, called vertices

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Graph Clustering

Graph Clustering. Why graph clustering is useful?. Distance matrices are graphs ? as useful as any other clustering Identification of communities in social networks Webpage clustering for better data management of web data. Outline. Min s-t cut problem Min cut problem Multiway cut

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Chapter 22: Elementary Graph Algorithms

Chapter 22: Elementary Graph Algorithms. Overview: Definition of a graph Representation of graphs adjacency list matrix Elementary search algorithms breadth-first search (BFS) depth-first search(DFS) topological sort strongly connected components. Notation.

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Flow Networks

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Graph Searching

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Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai

Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai Presented by : Yilin Shen Dept. Computer Information Science and Engineering University of Florida. Outline. Motivation: Power-law Networks Models , Measurement and Threat Taxonomy

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Deciding Equality with Uninterpreted Functions using Congruence Closure

Deciding Equality with Uninterpreted Functions using Congruence Closure. Constantinos Bartzis. The problem. Determine the validity of formulas like f(a,b)=a ? f(f(a, b), b)=a or, equivalently, satisfiability of f(a,b)=a ? f(f(a, b), b) ? a In 1954 Ackermann showed it is decidable.

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Lower Bounds for Additive Spanners, Emulators, and More

Lower Bounds for Additive Spanners, Emulators, and More. David P. Woodruff MIT. FOCS, 2006. The Model. G = (V, E) undirected unweighted graph, n vertices, m edges ? G (u,v) shortest path length from u to v in G Want to preserve pairwise distances ? G (u,v)

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Chapter 23: Minimum Spanning Trees: A graph optimization problem

Chapter 23: Minimum Spanning Trees: A graph optimization problem Given undirected graph G(V,E) and a weight function w(u,v) defined on all edges (u,v) ? E, find an acyclic subset T ? E that connects all the vertices and for which the total weight is a minimum w(T) = .

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CSCI 115

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Depth-First Search

A. B. D. E. C. Depth-First Search. Subgraphs. A subgraph S of a graph G is a graph such that The vertices of S are a subset of the vertices of G The edges of S are a subset of the edges of G A spanning subgraph of G is a subgraph that contains all the vertices of G. Subgraph.

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Weighted Graphs

Weighted Graphs. In a weighted graph, each edge has an associated numerical value, called the weight of the edge Edge weights may represent, distances, costs, etc. Example: In a flight route graph, the weight of an edge represents the distance in miles between the endpoint airports. 849.

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