Title: Multitarget search on complex networks: A logarithmic growth of global mean random cover time,
Abstract: We investigate multitarget search on complex networks and derive an exact
expression for the mean random cover time that quantifies the expected time a
walker needs to visit multiple targets. Based on this, we recover and extend
some interesting results of multitarget search on networks. Specifically, we
observe the logarithmic increase of the global mean random cover time with the
target number for a broad range of random search processes, including generic
random walks, biased random walks, and maximal entropy random walks. We show
that the logarithmic growth pattern is a universal feature of multi-target
search on networks by using the annealed network approach and the
Sherman-Morrison formula. Moreover, we find that for biased random walks, the
global mean random cover time can be minimized, and that the corresponding
optimal parameter also minimizes the global mean first passage time, pointing
towards its robustness. Our findings further confirm that the logarithmic
growth pattern is a universal law governing multitarget search in confined
media.