  The random sampling on graph signals is one of the fundamental topics in
graph signal processing. In this letter, we consider the random sampling of
k-bandlimited signals from the local measurements and show that no more than
O(klogk) measurements with replacement are sufficient for the accurate and
stable recovery of any k-bandlimited graph signals. We propose two random
sampling strategies based on the minimum measurements, i.e., the optimal
sampling and the estimated sampling. The geodesic distance between vertices is
introduced to design the sampling probability distribution. Numerical
experiments are included to show the effectiveness of the proposed methods.
