PPT-How do weights affects approximation algorithms?

How do weights affects approximation algorithms As usual there are no rules whatsoever However I will provide some interesting examples in which weights make a difference I will try and say for every problem why weights make a difference. 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. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. Ravishankar. . Krishnaswamy. (joint work with Nikhil . Bansal. and . Barna. . Saha. ). Approximating Set Cover. Given . m sets, n elements. Find . minimum cost. collection of sets . to cover . 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).. Alexander . Veniaminovich. IM. , . room. . 3. 44. Friday. 1. 7. :00. or. Saturday 14:30. Approximation. . algorithms. . 2. We will study. . NP. -. hard optimization problem. 3. What you should know. 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 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. Problem. Yan Lu. 2011-04-26. Klaus Jansen SODA 2009. CPSC669 Term Project—Paper Reading. 1. Problem Definition. 2. Approximation Scheme. 2.1 Instances with similar capacities. 2.2 General cases . Outline. 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.. and . Some Applications. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Based on joint work. Near-linear-time . approximation schemes for some implicit fractional packing problems.  . with . Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. 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. Lecture 18. May 29, . 2014. May 29, 2014. 1. CS38 Lecture 18. May 29, 2014. CS38 Lecture 18. 2. Outline. coping with . intractibility. approximation algorithms. set cover. TSP. center selection. randomness in algorithms. MST . and . metric-TSP Interdiction. Chaitanya Swamy. University of Waterloo. Joint work with . André . Linhares. University of Waterloo. Minimum spanning tree (MST) interdiction. Given: graph . G. =(V,.