Problem-solving using the extremality principle

Abstract

The extremality principle is one of the commonly used problem solving strategies. It involves looking at the extremal cases of a problem in order to obtain insight about the general structure. Though the principle is widely known, its use in designing algorithms is rarely discussed in CS literature. We present a methodology based on the extremality principle that is useful in solving a wide variety of algorithmic problems. We illustrate the effectiveness of the methodology by deriving solutions to three difficult problems. We believe that the key steps involved in our methodology can be taught to students as individual drills. We have anecdotal evidence for the teachability of the method.