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Graph Algorithms

Graph Algorithms. Andreas Klappenecker [based on slides by Prof. Welch]. Directed Graphs. Let V be a finite set and E a binary relation on V, that is, E ?VxV. Then the pair G=(V,E) is called a directed graph . The elements in V are called vertices . The elements in E are called edges .

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Graph Algorithms

Graph Algorithms. Andreas Klappenecker [based on slides by Prof. Welch]. Directed Graphs. Let V be a finite set and E a binary relation on V, that is, E ?VxV. Then the pair G=(V,E) is called a directed graph . The elements in V are called vertices . The elements in E are called edges .

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Image Synthesis

Image Synthesis. Shadows / Transparency. Inter-Object realism. Covers different kinds of interactions between objects Increasing realism in the scene Relationships between objects easier to understand Shadows, Reflections, Transparency. Shadow techniques .

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Linked Justifications: Provenance Aware Data Integration on Linked Data

Linked Justifications: Provenance Aware Data Integration on Linked Data. Li Ding Tetherless World Constellation Rensselaer Polytechnic Institute Nov 2, 2009. Linked Data. Data on the Web Use RDF Use dereferenceable HTTP URI Linked by typed links rdfs:seeAlso owl:sameAs ...

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Data Organization

Data Organization. Lots of Data Quickly Found. Image courtesy: http://www.flickr.com/photos/juhansonin/4734829999/sizes/o/in/photostream//. Organization. Are you an organized person? How much time would it take you to find your keys? a file on your computer? a phone number?

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Structure discovery in PPI networks using pattern-based network decomposition

Structure discovery in PPI networks using pattern-based network decomposition. Philip Bachman and Ying Liu BIOINFORMATICS System biology Vol.25 no. 14 2009 May 15, 2009. Outline. Introduction Graph-Theoretic concepts The algorithm Algorithm and results

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Trees and Connectivity

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Chapter 34B - Reflection and Mirrors II (Analytical)

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9.2 Graph Terminology and Special Types Graphs

9.2 Graph Terminology and Special Types Graphs. Basic Terminology Definition 1: Two vertices u and v in an undirected graph G are called adjacent (or neighbors ) in G if u and v are endpoints of an edge of G .

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The Landscape of Sparse Ax=b Solvers

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GRAPHS AND GRAPH TRAVERSALS 9/26/2000

COMP 6/4030 ALGORITHMS. GRAPHS AND GRAPH TRAVERSALS 9/26/2000. Graphs - Traversals. Task : visit all nodes of a (connected) graph G, starting from a given node. Equivalent formulation of this task : Find a spanning tree T of graph G starting from a given node. Definition

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5.5.3 Rooted tree and binary tree

5.5.3 Rooted tree and binary tree. Definition 25: A directed graph is a directed tree if the graph is a tree in the underlying undirected graph.

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Network Design with Degree Constraints

Network Design with Degree Constraints. Guy Kortsarz Joint work with R ohit Khandekar and Zeev Nutov. Problems we consider. Minimum cost 2- vertex-connected spanning subgraph with degree constraints Minimum-degree arborescence/tree spanning at least k vertices

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The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.

The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. diagram not to scale. Determine if this could be a right triangle. No, it could not. 1. The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm. Calculate the length of [AC]. 37.5 cm. 2. x = 1.28 m. 3.

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Packing Element-Disjoint Steiner Trees

Packing Element-Disjoint Steiner Trees. Mohammad R. Salavatipour Department of Computing Science University of Alberta Joint with Joseph Cheriyan Department of Combinatorics and Optimization University of Waterloo. The Problem. Given: Undirected graph G(V,E)

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Introduction Graphs

Vertices. Edges. Introduction Graphs . A graph G=(V,E) V =set of vertices (nodes) E =set of edges Examples : a map with cities connected by streets Cities are vertices Streets are edges Two basic types Undirected graphs (graphs) edge (u,v)=edge (v,u) Directed graphs (digraphs)

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How To Explore a Fast Changing World

How To Explore a Fast Changing World. (On the Cover Time of Dynamic Graphs). Chen Avin Ben Gurion University Joint work with Michal Koucky & Zvi Lotker (ICALP-08). Motivation.

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Platonic Solids

Platonic Solids. MATH 420 Presentation: Kelly Burgess. What are they?. Convex Polyhedron (polyhedron: 3d solid with straight edges and flat faces) All faces are congruent Same number of faces meet at each vertex Named after Greek philosopher Plato who associated each with a basic "element"

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