The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: What's Past is Prolog
A graduate student immediately set to work implementing dynamic programming to compare with their
heuristic. On many programs the optimal and greedy algorithms constructed the exact same trie.
However, for some examples, dynamic programming gave a 20% performance improvement over
greedy, i.e. 20% better than very, very well in practice. The run time spent in doing the dynamic
programming was sometimes a bit larger than with greedy, but in compiler optimization you are always
happy to trade off a little extra compilation time for better execution time performance of your program.
Is a 20% improvement worth it? That depends upon the situation. For example, how useful would you
find a 20% increase in your salary?
The fact that the rules had to remain ordered was the crucial property that we exploited in the dynamic
programming solution. Indeed, without it, I was able to prove that the problem was NP-complete,
something we put in the paper [DRR 95] to make it complete.
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