  Random search processes are instrumental in studying and understanding
navigation properties of complex networks, food search strategies of animals,
diffusion control of molecular processes in biological cells, and improving web
search engines. An essential part of random search processes and their
applications are various forms of (continuous or discrete time) random walk
models. The efficiency of a random search strategy in complex networks is
measured with the mean first passage time between two nodes or, more generally,
with the mean first passage time between two subsets of the vertex set. In this
paper we formulate a problem of adding a set of $k$ links between the two
subsets of the vertex set that optimally reduce the mean first passage time
between the sets. We demonstrate that the mean first passage time between two
sets is non-increasing and supermodular set function defined over the set of
links between the two sets. This allows us to use two greedy algorithms that
approximately solve the problem and we compare their performance against
several standard link prediction algorithms. We find that the proposed greedy
algorithms are better at choosing the links that reduce the navigation time
between the two sets.
