Now that you mention Donald Knuth, I can't resist sharing a really interesting answer he gave recently to one question from a set of twenty, related to algorith

Now that you mention Donald Knuth, I can't resist sharing a really interesting answer he gave recently to one question from a set of twenty, related to algorithm design and analysis [1]: 15. Robert Tarjan, Princeton: What do you see as the most promising directions for future work in algorithm design and analysis? What interesting and important open problems do you see? Don Knuth: My current draft about satisfiability already mentions 25 research problems, most of which are not yet well known to the theory community. Hence many of them might well be answered before Volume 4B is ready. Open problems pop up everywhere and often. But your question is, of course, really intended to be much more general. In general I'm looking for more focus on algorithms that work fast with respect to problems whose size, n, is feasible. Most of today's literature is devoted to algorithms that are asymptotically great, but they are helpful only when n exceeds the size of the universe. In one sense such literature makes my life easier, because I don't have to discuss those methods in TAOCP. I'm emphatically not against pure research, which significantly sharpens our abilities to deal with practical problems and which is interesting in its own right. So I sometimes play asymptotic games. But I sure wouldn't mind seeing a lot more algorithms that I could also use. For instance, I've been reading about algorithms that decide whether or not a given graph G belongs to a certain class. Is G, say, chordal? You and others discovered some great algorithms for the chordality and minimum fillin problems, early on, and an enormous number of extremely ingenious procedures have subsequently been developed for characterizing the graphs of other classes. But I've been surprised to discover that very few of these newer algorithms have actually been implemented. They exist only on paper, and often with details only sketched. Two years ago I needed an algorithm to decide whether G is a so-called comparability graph, and was disappointed by what had been published. I believe that all of the supposedly "most efficient" algorithms for that problem are too complicated to be trustworthy, even if I had a year to implement one of them. Thus I think the present state of research in algorithm design misunderstands the true nature of efficiency. The literature exhibits a dangerous trend in contemporary views of what deserves to be published. Another issue, when we come down to earth, is the efficiency of algorithms on real computers. As part of the Stanford GraphBase project I implemented four algorithms to compute minimum spanning trees of graphs, one of which was the very pretty method that you developed with Cheriton and Karp. Although I was expecting your method to be the winner, because it examines much of the data only half as often as the others, it actually came out two to three times worse than Kruskal's venerable method. Part of the reason was poor cache interaction, but the main cause was a large constant factor hidden by O notation. [1] http://www.informit.com/articles/article.aspx?p=2213858 http://www.informit.com/articles/article.aspx?p=2213858