PPT-1 Finding Sparser Directed Spanners

Piotr Berman Sofya Raskhodnikova Ge Ruan Pennsylvania State University Graph Spanners Awerbuch85Peleg Schäffer89 A subgraph H of G is a k spanner if for all pairs of vertices . We call the tail of the head of and uv the ends of If there is an edge with tail and head then we let uv denote such an edge and we say that this edge is directed from to Loops Parallel Edges and Simple Digraphs An edge uv in a digraph is a Euclidean Spanners: Short, Thin, andLanky Sunil Ary a  Gautam Das y David M. Moun tz Jerey S.Salo ex Mic hiel Euclidean spanners areimp ortan datastructures algorithm design, b ecausethey pro- vide Theconceptofspannerisabeautifulgraphtheoreticconceptinitsownright.Moreover,spannersarequiteusefulinvariousapplicationsintheareaofdistributedsystemsandcommunicationnetworks.Intheseapplications,spanners !!!. Cindy Bryant. LearnBop Director of Learning. cindy@learnbop.com. Agenda . Self-Directed Learning Fact or Fiction. Self-Directed Learner Characteristics. Benefits of Effective Self-Directed Learning. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs (intern). Based on a paper at . ICALP’11. , joint with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Dee Fraser. Providers & Personalisation. . Today…. Legislation. The Social Care (Self-directed Support) (Scotland) Act, 2013. The Self-directed Support (Direct Payments) Regulations, 2013. Statutory guidance for the Social Care (Self-directed Support) (Scotland) Act . . Character Positioning. Christine Talbot. Character Positioning. Discovery News – Avatar: Motion Capture Mirrors Emotions . http. ://. news.discovery.com. /videos/avatar-making-the-movie/. MindMakers. *. *. But were afraid to ask. Seth Pettie. University of Michigan,. Ann Arbor. What is a spanner?. Spanner (English) : wrench. Spanner (German) : voyeur, peeping tom.. Spanner (CS) : sparse . subgraph. A teacher who . needs. to know about . self-directed learning!. A teacher who knows about . self-directed learning!. Resourcing and Facilitating Self-directed Learning. How to work . SMARTER. not HARDER. Lee-Ad Gottlieb. Graph spanners. A spanner for graph G is a . subgraph. H. H contains vertices, subset of edges of G. Some qualities of a spanner. Degree, diameter, . stretch, weight. Applications: networks, routing, TSP… . What it is and why it matters. Bridget B. Matarazzo, Psy.D.. VISN 19 Mental Illness Research Education and Clinical Center; University of Colorado, School of Medicine, Department of Psychiatry. Developed in collaboration with the Centers for Disease Control and Prevention. Richard Peng. Georgia Tech. In collaboration with. Michael B. Cohen. Jon . Kelner. John Peebles. Aaron . Sidford. Adrian . Vladu. Anup. . B. Rao. Rasmus. . Kyng. Outline. Graphs and . Lx. = . b. G . 15851581158215771587157915841576158915831588157815801586Figure1CDFofselectivitiesfrom1SparkSQLqueriesonDatabricksthatreadJSONorCSVdataand2researchersqueriesoverJSONdataontheCensyssearchengine25Bothset JFK. BOS. MIA. ORD. LAX. DFW. SFO. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. Directed Graphs. 2. Digraphs. A . digraph.