Here "as quickly as the fastest algorithm" means: it takes at most 5x longer, plus a colossal enormous additive constant. To be a bit more precise, suppose you

Here "as quickly as the fastest algorithm" means: it takes at most 5x longer, plus a colossal enormous additive constant. To be a bit more precise, suppose you have a problem parameterized by some numbers a,b,c,...,z, and suppose there is some algorithm A that provably solves the problem, for any parameter values, in time T(a,b,c,...,z). Then Hutter's algorithm solves the problem im time at most 5T(a,b,c,...,z) + C where C, unfortunately, is something that looks like (smaller stuff) . 2^L where L is the length of the shortest proof that A solves the problem in time T(a,b,c,...,z). That timing information probably gives a clue as to how the algorithm works. Modulo oversimplification and handwaving, it enumerates all possible proofs of the form "such-and-such an algorithm solves the problem at takes at most such-and-such an amount of time to do it", and interleaves this with executing whatever algorithm it's currently got the best time bound for. There's a bit of subtlety in scheduling things so that it doesn't waste lots of time on what turn out to be worse algorithms. And that's basically it.