Algorithm Design Techniques

The September 1983 column described the " everyday " impact that algorithm design can have on programmers: an algorithmic view of a problem gives insights that may make a program simpler to understand and to write. In this column we'll study a contribution of the field that is less frequent but more impressive: sophisticated algorithmic methods sometimes lead to dramatic performance improvements. This column is built around one small problem, with an emphasis on the algorithms that solve it and the techniques used to design them. Some of the algorithms are a little complicated, but the complication is justified ; while the first algorithm we'll study takes 39 days to solve a problem of size 10,000, the final algorithm solves the same problem in just a third of a second.