  A frequent problem in settings where a unique resource must be shared among
users is how to resolve the contention that arises when all of them must use
it, but the resource allows only for one user each time. The application of
efficient solutions for this problem spans a myriad of settings such as radio
communication networks or databases. For the case where the number of users is
unknown, recent work has yielded fruitful results for local area networks and
radio networks, although either a (possibly loose) upper bound on the number of
users needs to be known, or the solution is suboptimal, or it is only implicit
or embedded in other problems, with bounds proved only asymptotically. In this
paper, under the assumption that collision detection or information on the
number of contenders is not available, we present a novel protocol for
contention resolution in radio networks, and we recreate a protocol previously
used for other problems, tailoring the constants for our needs. In contrast
with previous work, both protocols are proved to be optimal up to a small
constant factor and with high probability for big enough number of contenders.
Additionally, the protocols are evaluated and contrasted with the previous work
by extensive simulations. The evaluation shows that the complexity bounds
obtained by the analysis are rather tight, and that both protocols proposed
have small and predictable complexity for many system sizes (unlike previous
proposals).
