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Unformatted text preview: CS 435 : Linear Optimization Fall 2008 Lecture 19: Using LP techniques to design algorithms for combinatorial problems Lecturer: Sundar Vishwanathan Computer Science & Engineering Indian Institute of Technology, Bombay 1 Integer Linear Programs An Integer Linear Program is a linear program where the variables are constrained to take integer values only. Note that all variables have to take only integer values. An ILP can be written as max c T x Ax b x i is integral 8 i . The goal of this lecture is to present a technique for designing algorithms. We will give a template for designing algorithms and proving correctness. The template will come from linear programming; however the algorithms we design will be combinatorial. To understand the template, we will try designing an iterative algorithm for the linear programming problem: max c T x Ax b (1) The rst step is to nd some feasible solution. While this is in general as hard as solving an LP, for our examples this will be easy. For instance, ifexamples this will be easy....
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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