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Unformatted text preview: CS 435 : Linear Optimization Fall 2008 Lecture 20: Primal-dual algorithm for MST Lecturer: Sundar Vishwanathan Computer Science & Engineering Indian Institute of Technology, Bombay Our objective is to design combinatorial algorithms for speci c problems using hints from linear pro- gramming. Here are the main steps we will follow. 1. Write an ILP formulation of the problem. Remove the integrality constraint and write the dual. We may or may not need the dual. We will shortly see why. Depending on the problem we will work either with the primal or the dual. Suppose that the LP formunation we are working with is max c T x Ax b (1) 2. Find an initial feasible solution x . After the i th iteration, we will have a feasible solution x i . Note that this means Ax i b . 3. Design a combinatorial algorithm for the following problem. Let A be any subset of the rows of A . For the i th iteration, A will be the set of rows of A such that A x i = b . Find a y such that c T y > 0 and A y : Note: Sometimes, this may lead to unbounded optima. In which case weNote: Sometimes, this may lead to unbounded optima....
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This note was uploaded on 01/04/2010 for the course CSE CS435 taught by Professor Profsundar during the Summer '09 term at IIT Bombay.
- Summer '09
- Computer Science