A Guide to Solving Hard Problems

Abstract

In the previous chapters we have introduced a variety of algorithm design techniques and algorithmic concepts in order to attack hard problems. A lot of specific algorithms were presented in order to illustrate the power and possible success of their applications. Nevertheless, we did not consider the question

“What needs to be done when one is asked to solve a hard problem?”

up till now. We only listed a number of possible approaches and discussed what they can do and what they probably cannot do. The aim of this chapter is to discuss the search for a suitable method for solving a given problem depending on the requirements and constraints prescribed by the user. We present this discussion in a systematic way as follows.

“Discuss, commit errors, make mistakes, but for God’s sake think — even if you should be wrong — but think your own thoughts.”

Gotthold Ephrain Lessing