PPT-Applications of Treewidth in Algorithm Design

Daniel Lokshtanov Based on joint work with Hans Bodlaender Fedor FominEelko Penninkx Venkatesh Raman Saket Saurabh and Dimitrios Thilikos Background Most interesting graph problems are NPhard. 1 0 n 0 Error between 64257lter output and a desired signal Change the 64257lter parameters according to 1 57525u 1 Normalized LMS Algorithm Modify at time the parameter vector from to 1 ful64257lling the constraint 1 with the least modi6425 Grid-Minor Theorem. Chandra . Chekuri. , . Julia Chuzhoy. UIUC. . TTIC. Grid Minor Theorem . (Excluded Grid Theorem). [Robertson, Seymour ‘86]. Graph Minor Theory . [Robertson – Seymour]. Bucket elimination. Vibhav. . Gogate. Bucket Elimination: Initialization. A. B. C. D. E. F. (A,C). (C,E). (D,F). (B,D). (C,D). (A,B). You put each function . i. n exactly one bucket . Daniel Lokshtanov. Based on joint work with Hans Bodlaender ,Fedor Fomin,Eelko Penninkx, Venkatesh Raman, Saket Saurabh and Dimitrios Thilikos. Background. Most interesting graph problems are . NP-hard. Lower . Bounds Based on . SETH . D. ániel. Marx. (slides by Daniel . Lokshtanov. ). Simons Institute, Berkeley, CA. September 4. , 2015. Insert. «. Academic. unit» . on every page:. 1 Go to the menu «Insert». Parameterized complexity. Bounded tree width approaches. Juris . Viksna. , . 2015. Tree decomposition of graph. The purpose of the “−1” in the definition of the width of a decomposition is to let trees have tree width 1. Daniel Lokshtanov, UCSD. What is treewidth?. A graph parameter that measures how close a graph is to being a tree.. Graphs with . constant treewidth . share many properties with trees, this can be . exploited algorithmically. Constantinos (Costis) Daskalakis (MIT). . Yang Cai . (McGill). Matt Weinberg (Princeton). Algorithm. Algorithm Design. (desired). Output. (given). Input. Algorithm. Agents’. Reports. Agents’. Payoffs. The CU-GLASSES. KH . W. ong. The design of a smart glass for VR applications V1.a. 1. Introduction. Be able to overlay images or text to our normal view. Simple, low cost and easy to build. Can duplicate for the 2. “. Eighty percent of success is showing up.. ”. Woody Allen . “. Success is 1% inspiration and 99% perspiration.. ”. – Thomas Edison. . To successfully solve any problem, the most important step is to get actively involved.. Focus: developing algorithms . abstractly. Independent of programming . language, data types, etc.. Think of a stack or queue: not specific to C , but can be implemented when needed. Addressed in depth during COSC 320. 316. What is an . Algorithm. ?. A step by step procedure for calculations.. Pattern. Input -> output. Algorithm. exists everywhere. Military. Computer/programs. Medical field. Life. GAME. Algorithms. Algorithm is a step-by-step procedure, which defines a set of instructions to be executed in a certain order to get the desired output. Algorithms are generally created independent of underlying languages, i.e. an algorithm can be implemented in more than one programming language.. Adeetya's Kitchen & Furniture in Pune offers exquisite handmade furniture designs with superior craftsmanship and modern, stylish appeal. https://adeetyas.com/factory-made-furniture-design-in-pune.php