PPT-Submodular Set Function Maximization

A MiniSurvey Chandra Chekuri Univ of Illinois UrbanaChampaign Submodular Set Functions A function f 2 N R is submodular if fA fB fA B . Tel Aviv University Tel Aviv Israel nivbuchbindergmailcom Moran Feldman Computer Science Dept Technion Haifa Israel moranfecstechnionacil Joseph Sef64257 Naor Computer Science Dept Technion Haifa Israel naorcstechnionacil Roy Schwartz Theory Group M washingtonedu Jeff Bilmes Department of Electrical Engineering University of Washington bilmesuwashingtonedu Abstract We investigate two new optimization problems minimizing a submodular function subject to a submodular lower bound constraint submod Let denote the function de64257ned as follows First de64257ne a four parameter function by xyztabcd 2 43 Then xyzt 1 sin xyzt 1237566 54783217 1237896431 325123467 37 xyzt 5674235 4067231567 13245678 3748967543 2 xyzt 3867435523 7134893 75 35658 Honglei. . Zhuang. , . Yihan. Sun, Jie Tang, Jialin Zhang, Xiaoming Sun. Influence Maximization. 0.6. 0.5. 0.1. 0.4. 0.6. 0.1. 0.8. 0.1. A. B. C. D. E. F. Probability . of . influence. Marketer Alice. . Tripathi. Georgia Institute of Technology. Approximability. of Combinatorial Optimization Problems with . Submodular. Cost Functions. Based on joint work with . Gagan. . Goel. , . Chinmay. . Karande. Lecture 5 – Part 1. M. Pawan Kumar. pawan.kumar@ecp.fr. Slides available online http://. cvn.ecp.fr. /personnel/. pawan. /. Submodular. Functions. Examples. Outline. Submodular. Function. Set S. Function f over power set of S. A Mini-Survey. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Submodular Set Functions. A function . f. : 2. N. . . . R . is submodular if. . f(A. ) + . f(B. ) ≥ . f(A. . B. ) + . general . submodular. functions. CVPR 2015 . Tutorial. Stefanie Jegelka. MIT. The set function view. 2. cost. of buying items . together, or. utility, . or. probability, …. (. . ). submodular. . objectives: . continuous extensions . &. . dependent . randomized . rounding. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Combinatorial Optimization. N. a finite ground set. Reading Group. Submodular. Function Minimization. via Linear Programming. M. Pawan Kumar. http://. www.robots.ox.ac.uk. /~oval/. Separation and Optimization. Submodular. Function Minimization. Outline. Dictionary Selection. for Sparse Representation. Volkan . Cevher. volkan.cevher@epfl.ch. Laboratory. for Information . . and Inference Systems - . LIONS. & . Idiap. Research Institute. . Joint work with . of . submodular. and XOS . functions by juntas. Vitaly. Feldman and Jan . Vondrâk. IBM . Research - . Almaden. Prelims:. Submodular. and XOS. Functions; . Learning. $20. $27. Approximation by juntas. Unconstrained Submodular Maximization Moran Feldman The Open University of Israel Based On Maximizing Non-monotone Submodular Functions. Uriel Feige , Vahab S. Mirrokni and Jan Vondrák , SIAM J. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. Maria . Florina. . Balcan. LGO, . 11/16/2010. f(S)+f(T) . ¸. f(S . Å. T) + f(S . [. T), .