A convex principle of search time for a multi-biased random walk on complex networks

Abstract We propose a mixed strategy named multi-biased random walk on complex networks, i.e., a walker simultaneously adopts different biased random walks with respective proportions. An analytical expression of mean first passage time is derived to quantify the expected time required to find a given target. The global mean first passage time of our strategy turns out to obey a convex function with respect to that of their associated pure strategies no matter the target is static or mobile. It is a fundamental law governing this mixed search strategy. These findings are confirmed by numerical and theoretical results on a number of synthetic and real networks.