A flaw in the greedy approximation algorithm proposed by Zhang et al. for
minimum connected set cover problem is corrected, and a stronger result on the
approximation ratio of the modified greedy algorithm is established. The
results are now consistent with the existing results on connected dominating
set problem which is a special case of the minimum connected set cover problem.
We analyze the multihop delay of ad hoc cognitive radio networks, where the
transmission delay of each hop consists of the propagation delay and the
waiting time for the availability of the communication channel (i.e., the
occurrence of a spectrum opportunity at this hop). Using theories and
techniques from continuum percolation and ergodicity, we establish the scaling
law of the minimum multihop delay with respect to the source-destination
distance in cognitive radio networks.