Approximation Algorithms

Slides:



Advertisements
Similar presentations
Instructor Neelima Gupta Table of Contents Approximation Algorithms.
Advertisements

O(N 1.5 ) divide-and-conquer technique for Minimum Spanning Tree problem Step 1: Divide the graph into  N sub-graph by clustering. Step 2: Solve each.
Design and Analysis of Algorithms Approximation algorithms for NP-complete problems Haidong Xue Summer 2012, at GSU.
Lecture 24 Coping with NPC and Unsolvable problems. When a problem is unsolvable, that's generally very bad news: it means there is no general algorithm.
Introduction to Algorithms
3.5 Using the Properties of Parallel lines Making Lines Parallel.
Approximation Algorithms for TSP
Chapter 10 Complexity of Approximation (1) L-Reduction Ding-Zhu Du.
PCPs and Inapproximability Introduction. My T. Thai 2 Why Approximation Algorithms  Problems that we cannot find an optimal solution.
Linear Learning Machines  Simplest case: the decision function is a hyperplane in input space.  The Perceptron Algorithm: Rosenblatt, 1956  An on-line.
1 Approximation Algorithms for Demand- Robust and Stochastic Min-Cut Problems Vineet Goyal Carnegie Mellon University Based on, [Golovin, G, Ravi] (STACS’06)
CPSC 689: Discrete Algorithms for Mobile and Wireless Systems Spring 2009 Prof. Jennifer Welch.
Graph Triangulation by Dmitry Pidan Based on the paper “A sufficiently fast algorithm for finding close to optimal junction tree” by Ann Becker and Dan.
A general approximation technique for constrained forest problems Michael X. Goemans & David P. Williamson Presented by: Yonatan Elhanani & Yuval Cohen.
Gomory-Hu Tree for representation of minimum cuts Elad Avni.
1 Combinatorial Dominance Analysis Keywords: Combinatorial Optimization (CO) Approximation Algorithms (AA) Approximation Ratio (a.r) Combinatorial Dominance.
Graph-Cut Algorithm with Application to Computer Vision Presented by Yongsub Lim Applied Algorithm Laboratory.
Grace Hopper Celebration of Women in Computing Evaluating Algorithmic Design Paradigms Sashka Davis Advised by Russell Impagliazzo UC San Diego October.
Constant Factor Approximation of Vertex Cuts in Planar Graphs Eyal Amir, Robert Krauthgamer, Satish Rao Presented by Elif Kolotoglu.
Outline Introduction The hardness result The approximation algorithm.
Equations of Circles 10.6 California State Standards 17: Prove theorems using coordinate geometry.
A linear time algorithm for recognizing a K 5 -minor Bruce Reed Zhentao Li.
Section 5.3 – The Definite Integral
Spectral graph theory Network & Matrix Computations CS NMC David F. Gleich.
Computational Molecular Biology Non-unique Probe Selection via Group Testing.
Chapter 7 Similarity. Definition: Ratio The angles of a pentagon are in ratio 4:2:5:5:2, find the measure of each angle 4x+2x+5x+5x+2x = x.
 Rooted tree and binary tree  Theorem 5.19: A full binary tree with t leaves contains i=t-1 internal vertices.
5.5.2 M inimum spanning trees  Definition 24: A minimum spanning tree in a connected weighted graph is a spanning tree that has the smallest possible.
1. Prove the Pythagorean Theorem by a method not used in class.. § 12.1 There are over 260 of them. You should not have had too much trouble finding another.
3.3 Parallel Lines & Transversals
Lecture19: Graph III Bohyung Han CSE, POSTECH CSED233: Data Structures (2014F)
WK15. Vertex Cover and Approximation Algorithm By Lin, Jr-Shiun Choi, Jae Sung.
Computational Molecular Biology Non-unique Probe Selection via Group Testing.
Vasilis Syrgkanis Cornell University
Introduction to Algorithms All-Pairs Shortest Paths My T. UF.
MA Day 30 - February 18, 2013 Section 11.7: Finish optimization examples Section 12.1: Double Integrals over Rectangles.
Ch 3.1 Standard 2.0: Students write geometric proofs. Standard 4.0: Students prove basic theorems involving congruence. Standard 7.0: Students prove and.
Approximation Algorithms Duality My T. UF.
Computational Molecular Biology
5.6 Prefix codes and optimal tree Definition 31: Codes with this property which the bit string for a letter never occurs as the first part of the bit string.
Computational Molecular Biology Pooling Designs – Inhibitor Models.
Introduction to Algorithms
Optimization problems such as
Minimum Spanning Tree Chapter 13.6.
Exercise Exercise Proof that
CS4234 Optimiz(s)ation Algorithms
Computational Molecular Biology
Spectral Clustering.
Approximating k-route cuts
Approximation Algorithms for TSP
k-center Clustering under Perturbation Resilience
CS200: Algorithm Analysis
Connected Components Minimum Spanning Tree
Lecture 9 Greedy Strategy
Graph Partitioning Problems
Modular Arithmetic and Change of Base
3.5 Minimum Cuts in Undirected Graphs
4-4 Graph Theory Trees.
Kruskal’s Algorithm for finding a minimum spanning tree
CSE322 Minimization of finite Automaton & REGULAR LANGUAGES
Approximation Algorithms

Computational Molecular Biology
Clustering.
Minimum Spanning Trees (MSTs)
Lecture 28 Approximation of Set Cover
Constructing a m-connected k-Dominating Set in Unit Disc Graphs
at University of Texas at Dallas
Lecture 24 Vertex Cover and Hamiltonian Cycle
Proving Statements about Segments
Presentation transcript:

Approximation Algorithms k-Center

Definition ≤ My T. Thai mythai@cise.ufl.edu

2-Approx My T. Thai mythai@cise.ufl.edu

My T. Thai mythai@cise.ufl.edu

My T. Thai mythai@cise.ufl.edu

Analysis My T. Thai mythai@cise.ufl.edu

Obtain Better Ratio? My T. Thai mythai@cise.ufl.edu

Weighted k-Center My T. Thai mythai@cise.ufl.edu

Notations My T. Thai mythai@cise.ufl.edu

Algorithm My T. Thai mythai@cise.ufl.edu

Algorithm 2 My T. Thai mythai@cise.ufl.edu

Analysis Theorem: Alg 2 has an approx ratio of 3. My T. Thai mythai@cise.ufl.edu

Multiway Cut and k-Cut My T. Thai mythai@cise.ufl.edu

Definition My T. Thai mythai@cise.ufl.edu

Example My T. Thai mythai@cise.ufl.edu

Can you prove it??? My T. Thai mythai@cise.ufl.edu

Approximation My T. Thai mythai@cise.ufl.edu

Analysis My T. Thai mythai@cise.ufl.edu

Minimum k-cut Problem My T. Thai mythai@cise.ufl.edu

Example My T. Thai mythai@cise.ufl.edu

Construct a Gomory-Hu Tree My T. Thai mythai@cise.ufl.edu

My T. Thai mythai@cise.ufl.edu

Properties of Gomory-Hu Tree wrt k-cut My T. Thai mythai@cise.ufl.edu

Approximation Algorithm My T. Thai mythai@cise.ufl.edu

Analysis My T. Thai mythai@cise.ufl.edu

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.