Greedy reduction of navigation time in random search processes

Abstract: 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.