  Is it possible to find a shortest description for a binary string? The
well-known answer is "no, Kolmogorov complexity is not computable." Faced with
this barrier, one might instead seek a short list of candidates which includes
a laconic description. Remarkably such approximations exist. This paper
presents an efficient algorithm which generates a polynomial-size list
containing an optimal description for a given input string. Along the way, we
employ expander graphs and randomness dispersers to obtain an Explicit Online
Matching Theorem for bipartite graphs and a refinement of Muchnik's Conditional
Complexity Theorem. Our main result extends recent work by Bauwens, Mahklin,
Vereschchagin, and Zimand.
