PPT-Approximation Algorithms for Graph Routing Problems

Julia Chuzhoy Toyota Technological Institute at Chicago Routing Problems Input Graph G sourcesink pairs s 1 t 1 s k t k Goal Route as many pairs as possible minimize edge congestion. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. 1. Graph Algorithms. Many problems are naturally represented as graphs. Networks, Maps, Possible paths, Resource Flow, etc.. Ch. 3 focuses on algorithms to find connectivity in graphs. Ch. 4 focuses on algorithms to find paths within graphs. 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).. 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. Spanner of Directed Graphs. Kyomin. Jung. KAIST. 2009 . Combinatorics. Workshop. Joint work with . A. rnab. Bhattacharyya . MIT. . Elena . Grigorescu. . MIT. . . 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. Problems. Proofs. Approximations. Decision Problems. Given Some Universal Set X,. Let R be a subset of X.. The decision problem for R is:. Given an arbitrary element a of X, does. a belong to R?. Note: X is usually assumed to be a set of . Guo QI, Chen Zhenghai, Wang Guanhua, Shen Shiqi, Himeshi De Silva. Introduction. Shen Shiqi. Definition. Approximation . Algorithm. Return . the solutions to optimization problem. Comparison. Approximation . 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. Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. -Poulin - 4073219. CEG 4136 – Computer Architecture III. November 16. th. , 2010. Questions/Topics. Describe several algorithms used for adaptive . routing.. Describe . problems and advantages of these routing . Data Structures and Algorithms. CSE 373 WI 19 - Kasey Champion. 1. Last Time. We described algorithms to find:. CSE 373 SP 18 - Kasey Champion. 2. An ordering of the vertices so all edges go from left to right. . Data Structures and Algorithms. CSE 373 19 . Sp. - Kasey Champion. 1. Administrivia. HW 7 Due Friday. Final exam review Wednesday 6/5 4-5:50. Final exam next Tuesday!. Double check all grades . Please fill out survey. 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..