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Chapter 19 Linear Programming in Low Dimensions

In this chapter, we shortly describe (and analyze) a simple randomized algorithm for linear programming in low dimensions. Next, we show how to extend this algorithm to solve linear programming with violations. Finally, we will show how one can efficiently approximate the number constraints that one needs to violate to make a linear program feasible. This serves as a fruitful ground to demonstrate some of the techniques we visited already. Our discussion is going to be somewhat intuitive – it can be made more formal with more work.