PPT-PRIMAL-DUAL APPROXIMATION ALGORITHMS FOR METRIC FACILITY LO

AND KMEDIAN PROBLEMS K Jain V Vazirani Journal of the ACM 2001   PRIMALDUAL APPROACH We start by constructing a primal problem. HOCHBAUM University of California Berkeley Calijornia AND DAVID B SHMOYS Mussuchasetts Institute of Technology Cambridge Massachusetts Abstract The problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. . Chandrasekaran. Harvard University. A Polynomial-Time Cutting-Plane Algorithm . for . Matchings. Cutting Plane Method.  .  .  .  .  .  .  .  .  .  .  . Cutting Plane Method. Starting LP.. Lecture 9. N. Harvey. http://www.math.uwaterloo.ca/~harvey/. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. A. A. A. Outline. Complementary Slackness. Mathematical Programming. Fall 2010. Lecture 5. N. Harvey. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. A. A. A. Review of our Theorems.  . Subject. to.  . ..  . ..  . Duality. Minimize.  . Subject. to.  . ..  . ..  . Primal. :. Dual:. Maximize. Subject. to.  . Duality. Minimize. Subject. to. Primal. :. Dual:. .  .  . . Prof. Andy Mirzaian. Linear . Programming. . General Overview. Introduction. Fundamentals. Duality. Major Algorithms. Open Problems. . 2D Linear Programming. . O(n log n) time by computation of feasible region. 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. Seffi. . Naor. Computer Science Dept.. Technion. . Barriers in Computational Complexity II Workshop 8/2010. Joint papers: Nikhil . Bansal. , . Niv. . Buchbinder. , . Kamal. Jain. Online Algorithms / Competitive Analysis. : MRF inference via the primal-dual schema. Nikos . Komodakis. . Tutorial at ICCV . (Barcelona, Spain, November 2011). The primal-dual schema. Say we seek an optimal solution . x*. to the following integer program (this is our . 1. . . If x. i. . ≠ 0,. . i. = 1, 2, … , n the . ith. dual . equation is tight. .. 2. If . equation . i. of the primal . is not tight, . y. i. =0.. 1. Complementary Slackness Theorem (5.2): . 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. . Set Cover. Set Cover. Given. a universe . U . of. . n . elements. , . a collection of subsets of . U. , . S. = . {. S. 1. ,…,. . S. k. }, and a cost function . c. : . S. . → . Q. +. .. Find . Semidefinite. Programming. Satyen. Kale . (Yahoo! Research). Joint work with. Sanjeev. . Arora. . (Princeton). Semidefinite. Programming. Semidefinite. Program (SDP):. find . X. . s.t.. .