PPT-A Simple ¾-Approximation Algorithm for MAX SAT

David P Williamson Joint work with Matthias Poloczek Cornell Georg Schnitger Frankfurt and Anke van Zuylen William amp Mary Greedy algorithms Greed for lack of a better word is good Greed is right Greed works. 2 02 02 02 Flash point TOC F T 79 100 150 150 150 Distillation test T 78 Distillate percentage by volume of tota l distillate to 680F to 437F 25 10 to 500F 40 70 15 55 35 15 to 600F 75 93 60 87 45 80 15 75 Residue from distillation volume Approximation . Algorithms. II. How. to . find. a heavy . weight. . cut. in a . graph. The MAX CUT Problem. Given an . undirected. . graph. G=(V,E) with . edge. . weights. . w:E->R. , . divide. Matt Weinberg. MIT .  Princeton  MSR. References: . . http. ://arxiv.org/abs/. 1305.4002. http. ://arxiv.org/abs/. 1405.5940. http. ://arxiv.org/abs/. 1305.4000. Recap. Costis. ’ Talk: . Optimal multi-dimensional mechanism: additive bidders, no constraints. Princeton University. Game Theory Meets. Compressed Sensing. Based on joint work with:. Volkan. Cevher. Robert. Calderbank. Rob. Schapire. Compressed Sensing. Main tasks:. Design a . sensing . matrix. SUN SUN SUN SUN SUN SUN MON MON MON MON MON MON TUE TUE TUE TUE TUE TUE WED WED WED WED WED WED THU THU THU THU THU THU FRI FRI FRI FRI FRI FRI APRIL JUNE AUGUST MAY JULY SEPTEMBER SAT SAT SAT SAT SAT 1. Tsvi. . Kopelowitz. Knapsack. Given: a set S of n objects with weights and values, and a weight bound:. w. 1. , w. 2. , …, w. n. , B (weights, weight bound).. v. 1. , v. 2. , …, v. n. (values - profit).. !max mge2!T+2max mge!Tmax mg0(13)x0+_x0 !+max mge2!T2max mge!T+max mg0(14)Ifweassumetheworst-case,T=Tmax,thentheinequalitiesfromabovebecomemax mg(e!Tmax1)2x0+_x0 !++max mg(e!Tma Sometimes we can handle NP problems with polynomial time algorithms which are guaranteed to return a solution within some specific bound of the optimal solution. within a constant . c. . of the optimal. 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 . Algorithms. and Networks 2015/2016. Hans L. . Bodlaender. Johan M. M. van Rooij. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. A. A. What to do if a problem is. 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. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. When the best just isn’t possible. Jeff Chastine. Approximation Algorithms. Some NP-Complete problems are too important to ignore. Approaches:. If input small, run it anyway. Consider special cases that may run in polynomial time. and Matroids. Soheil Ehsani. January 2018. Joint work with M. . Hajiaghayi. , T. . Kesselheim. , S. . Singla. The problem consists of an . initial setting . and a . sequence of events. .. We have to take particular actions .