PPT-Routing in Undirected Graphs with Constant Congestion

Julia Chuzhoy Toyota Technological Institute at Chicago Routing Problems Input Graph G sourcesink pairs s 1 t 1 s k t k Goal Route as many pairs as possible minimize edge congestion. In this note we give a similar result for the diameter of strongly connected directed graphs namely 2max log1 57374 log 1 where is the 57356rst nontrivial eigenvalue of the Laplacian and is the Perron vector of the transition probability matrix of June . 9. , 2015. Carnegie Mellon University. Center for . Causal. . Discovery. Outline. Day 2: Search. Bridge Principles: . Causation. .  . Probability. D-separation. Model Equivalence. Search Basics (PC, GES). Wireless Mesh Networks. A. Bhorkar. University Qualifying Examination. University of California, San Diego. Motivation. 2. Wireless Mesh Networks. . Characteristics. :. Fixed, unlimited energy, virtually unlimited processing power. What is a graph?. Directed vs. undirected graphs. Trees vs graphs. Terminology: Degree of a Vertex . Graph terminology. Graph Traversal. Graph representation. Topics to be discussed…. What is a graph?. Graphs 1. Graphs. Definition:. Two types: . Undirected. Directed. Examples/Applications. Transportation Networks. Source: pages.cs.wisc.edu. Shortest path?. Vacuum World (from AI). Source: . centurion2.com. Graphs. Goals . Introduction and Motivation. Representations. Why do we care about graphs?. Many Applications. Social Networks – Facebook. Video Games - Motion Graphs. Machine Learning/AI . Delivery Networks/Scheduling – UPS?. Julia Chuzhoy. Toyota Technological Institute at Chicago. Routing Problems. Input. : Graph G, source-sink pairs (s. 1. ,t. 1. ),…,(. s. k. ,t. k. ).. Goal. : Route as many pairs as possible; minimize edge congestion.. Addressing routing scalability issues. NSF Ignite Project . 1. Routing protocol challenges . All Routing . P. rotocols face. S. calability issues – dependency on network size. Flooding on information changes. Haim. Kaplan . – . Tel Aviv Univ. . . Mikkel. . Thorup. . – Univ. of Copenhagen . Uri . Zwick. . – Tel Aviv Univ.. Adjacency labeling schemes . and. induced-universal graphs. TexPoint fonts used in EMF. . Quarter: Summer 2017. CSE 373: Data Structures and Algorithms. Lecture . 14: Introduction to Graphs. Today. Overview of Midterm. Introduce Graphs. Mathematical representation. Undirected & Directed Graphs. Announcements. A5 Heaps Due October 27. Prelim 2 in ~3 weeks: Thursday Nov 15. A4 being graded right now. Mid-Semester College Transitions Survey on Piazza. 2. These aren't the graphs we're looking for. GRAPHS Lecture 17 CS 2110 — Spring 2019 JavaHyperText Topics “Graphs”, topics 1-3 1: Graph definitions 2: Graph terminology 3: Graph representations 2 Charts (aka graphs) Graphs Graph: [charts] Routing Distance Vector (DV) Routing Sets up minimum distance routes to all nodes in a network Routing tables created at each node with following fields: The core algorithm is based on ‘ Bellman Ford shortest path algorithm & . Multiroute. Flows. Chandra Chekuri. . . Univ. of Illinois, Urbana-Champaign. Joint work with . Mark . Idleman. s-t flows in directed graphs. G=(V,E) . directed graph . with edge capacities .