Denef and Douglas have observed that in certain landscape models the problem
of finding small values of the cosmological constant is a large instance of an
NP-hard problem. The number of elementary operations (quantum gates) needed to
solve this problem by brute force search exceeds the estimated computational
capacity of the observable universe. Here we describe a way out of this
puzzling circumstance: despite being NP-hard, the problem of finding a small
cosmological constant can be attacked by more sophisticated algorithms whose
performance vastly exceeds brute force search. In fact, in some parameter
regimes the average-case complexity is polynomial. We demonstrate this by
explicitly finding a cosmological constant of order 10−120 in a randomly
generated 109-dimensional ADK landscape.Comment: 19 pages, 5 figure