PPT-An introduction to Treewidth

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. Introduction:Introduction: Introduction:Introduction:A hard concept to sellA hard concept to sell Making sure the combat doesn for Computing . Treewidth. Bart M. P. Jansen. Insert. «. Academic. unit» . on every page:. 1 Go to the menu «Insert». 2 Choose: Date and time. 3 Write the name of your faculty or department in the field «Footer». 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 . 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 . Bart M. P. . Jansen . Daniel Lokshtanov . University of Bergen, Norway. Saket Saurabh. Institute of Mathematical Sciences, India. Insert. «. Academic. unit» . on every page:. 1 Go to the menu «Insert». Pathwidth. Bart M. P. Jansen. Joint work with . Hans L. . Bodlaender. & Stefan . Kratsch. July 6th 2012, SWAT 2012, Helsinki. What is . pathwidth. ?. 2. What is . pathwidth. ?. Measure of how “path-like” a graph is. , Applications, and . some Recent Developments. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Goals of Tutorial. Give an intuitive understanding of . treewidth. and . tree . decompositions. 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. 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. : . Structure . and . Algorithms*. Presented By:. Saleh. A. . Almugrin. salmugri@kent.edu. * Based . and influenced by . many works of . Hans L. . Bodlaender. , . Institute of Information and Computing Sciences, Utrecht . Minors, . Bidimensionality. ,. & Decomposition. r. r. Erik Demaine. MIT. Goals. How far . beyond planar graphs . can we go?. Graphs excluding. a fixed minor. Powers thereof. Build . general approximation frameworks . Radu Curticapean, Holger Dell, Dániel Marx. NEW INSIGHTS INTO. Saarland University,. Cluster . of. Excellence (MMCI). Institute . for. Computer Science . and. Control,. Hungarian. Academy . of. 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.