  Star sampling (SS) is a random sampling procedure on a graph wherein each
sample consists of a randomly selected vertex (the star center) and its
(one-hop) neighbors (the star points). We consider the use of SS to find any
member of a target set of vertices in a graph, where the figure of merit (cost)
is either the expected number of samples (unit cost) or the expected number of
star centers plus star points (linear cost) until a vertex in the target set is
encountered, either as a star center or as a star point. We analyze these two
performance measures on three related star sampling paradigms: SS with
replacement (SSR), SS without center replacement (SSC), and SS without star
replacement (SSS). Exact and approximate expressions are derived for the
expected unit and linear costs of SSR, SSC, and SSS on Erd\H{o}s-R\'{e}nyi (ER)
random graphs. The approximations are seen to be accurate. SSC/SSS are notably
better than SSR under unit cost for low-density ER graphs, while SSS is notably
better than SSR/SSC under linear cost for low- to moderate-density ER graphs.
Simulations on twelve "real-world" graphs shows the cost approximations to be
of variable quality: the SSR and SSC approximations are uniformly accurate,
while the SSS approximation, derived for an ER graph, is of variable accuracy.
