PPT-Approximation for Directed Spanner

Grigory Yaroslavtsev Penn State ATampT Labs intern Based on a paper at ICALP11 joint with Berman PSU Bhattacharyya MIT Makarychev IBM Raskhodnikova PSU. 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 Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . By. - . James C. Corbett, Jeffrey Dean, Michael Epstein, Andrew . Fikes. , Christopher Frost, JJ Furman. Sanjay . Ghemawat. , . Andrey. . Gubarev. , Christopher . Heiser. , Peter . Hochschild. , Wilson Hsieh,. 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… . Piotr. Berman, . Sofya. . Raskhodnikova. , . Ge. . Ruan. Pennsylvania . State University. Graph Spanners . [Awerbuch85,Peleg Schäffer89]. A . subgraph. . H. of . G . is a . k. -spanner. . if for all pairs of vertices . Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. Spanner of Directed Graphs. Kyomin. Jung. KAIST. 2009 . Combinatorics. Workshop. Joint work with . A. rnab. Bhattacharyya . MIT. . Elena . Grigorescu. . MIT. . . 1) . M. Hajiaghayi, . Khandekar. and K.. 2) . M. . Cygan. ,. K. 3) . R . Chitnis. , . M. Hajiaghayi. ,. K . 4) . M. Hajiaghayi, K and some students of M. Hajiaghayi. Optimal running times for exact solutions and approximated solutions. L. inear Time Algorithm for Computing a . -Spanner of . Size in Weighted Graphs.  . Surender. . Baswana. and Sandeep Sen. Slides and Presentation By: . Nadav. Hollander. So, what exactly is a. -spanner. James C. Corbett et al . OSDI 2012. Presenter: Akshay Ravichandran. Outline. What is Spanner?. Why Spanner?. Implementation. External Consistency. Concurrency Control. Evaluation. Related Work. Future Work. δ. -Timeliness. Carole . Delporte-Gallet. , . LIAFA . UMR 7089. , Paris VII. Stéphane Devismes. , VERIMAG UMR 5104, Grenoble I. Hugues Fauconnier. , . LIAFA . UMR 7089. , Paris VII. LIAFA. Motivation. Yair. . Bartal. . Hebrew University. Lee-Ad Gottlieb. . Ariel University. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . AAAA. Traveling salesman problem. Definition:. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. System. David F. Bacon et al. . Google, Inc. . Presenter: Che-Lin Huang. Overview. Motivation. Introduction to Spanner. Distributed . Query. Query Range . Extraction. Query . Restart. Common SQL . Dialect.