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. . 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. 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. Johnnie B. Linn . III. . Concord . University, Athens, WV. Creative Destruction as Industrial Mutation. The opening up of new markets, foreign or domestic, and the organizational development from the craft shop and factory to such concerns as U.S. Steel illustrate the same process of . 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 . 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 . Semidefinite. Programming. Satyen. Kale . (Yahoo! Research). Joint work with. Sanjeev. . Arora. . (Princeton). Semidefinite. Programming. Semidefinite. Program (SDP):. find . X. . s.t.. . 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. Julia Chuzhoy. Toyota Technological Institute at Chicago. Routing Problems. Input. : Graph G, source-sink pairs (s. 1. ,t. 1. ),…,(. s. k. ,t. k. ).. Goal. : Route as many pairs as possible; minimize edge congestion.. 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. What do we measure most in science?. English. Metric. Metric Symbol. Foot. Volume. Gallon. Pound. Temperature. Fahrenheit. Metric system. What do we measure most in science?. English. Metric. Metric Symbol.