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Drmota and A Llado Institute of Discrete Mathematics and Geometry Vienna University of Technology Vienna Austria Dept Matematica Aplicada 4 Universitat Politecnica de CatalunyaBarcelonaTech Barcelona Spain Abstract We show that asymptotically almost. The Swan Hill fruitless olive tree has quickly gained in popularity. It's attractive foliage and form is enhanced by its absence of fruit, and makes its use in entryways and other high foot-traffic areas a plus. Olives, after all, are best in martinis, on pizza or enjoyed at the table one by one. 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. . Spanning Trees. CSE 680. Prof. Roger Crawfis. Tree. We call an undirected graph a . tree . if the graph is . connected . and. . contains . no cycles. .. Trees:. Not Trees:. Not connected. Has a . CS648. . Lecture 17. Miscellaneous applications of . Backward analysis. 1. Minimum spanning tree. 2. Minimum spanning tree. . 3. b. a. c. d. h. x. y. u. v. 18. 7. 1. 19. 22. 10. 3. 12. 3. 15. 11. 5. 1. Uri Zwick. Tel Aviv University. October 2015. Last updated. : November 18, . 2015. Spanning Trees. 2. A . tree. is a . connected. . acyclic . graph (contains no . cycles. ). .. A . spanning tree . Agenda. Introduction to the Bimodal IT Function. Insights from this Research into Bimodal IT. Navigating the IT Transformation Journey. Guidelines for Transforming the IT Function. Moving Beyond Bimodal IT. like me to cover on . Thursday. Asymptotic Notation. Binary. Search. T(n)=T(n/2) O(1). O(log. n). Merge Sort. T(n)=2T(n/2) O(n). O(n log n). Towers of Hanoi. T(n)=2T(n-1) O(1). O(2. n. ). Integer. Multiplication (. . Spanning Trees. CSE 680. Prof. Roger Crawfis. Tree. We call an undirected graph a . tree . if the graph is . connected . and. . contains . no cycles. .. Trees:. Not Trees:. Not connected. Has a . Common Names. Archaebacteria. Archaea. Oldest bacteria. Methanogens. , . Halophiles. , . Thermoacidophiles. Eubacteria. Bacteria. Newer bacteria. Decomposes, parasites, . cyanobacteria. , nitrogen-fixation bacteria. Thanks to Kasey Champion, Ben Jones, Adam Blank, Michael Lee, Evan McCarty, Robbie Weber, Whitaker Brand, Zora Fung, Stuart . Reges. , Justin Hsia, Ruth Anderson, and many others for sample slides and materials .... MST . and . metric-TSP Interdiction. Chaitanya Swamy. University of Waterloo. Joint work with . André . Linhares. University of Waterloo. Minimum spanning tree (MST) interdiction. Given: graph . G. =(V,. Minimum Spanning Tree. Shortest Path with negative edge length. What is w(. u,v. ) can be negative?. Motivation: Arbitrage. Image from . wikipedia. Modeling arbitrage. Suppose . u, v . are different currency, exchange rate is . for. . (. s,t. )-. mincuts. Surender Baswana. Department of CSE, IIT Kanpur. Joint work with . Koustav. . Bhanja. Research supported by . Tapas Mishra Memorial Chair. (. ,. ). -. cut.  . ,. . with. BFS Structure. Merav. . Parter. . and David . Peleg. Weizmann Institute of Science, Israel. SODA 2014. Breadth First Search (BFS) Trees. Shortest-Path Tree . (BFS) rooted at. s. .. Sparse solution: .