  Pliable index coding considers a server with m messages, and n clients where
each has as side information a subset of the messages. We seek to minimize the
number of transmissions the server should make, so that each client receives
(any) one message she does not already have. Previous work has shown that the
server can achieve this using O(\log^2(n)) transmissions and needs at least
\Omega(log(n)) transmissions in the worst case, but finding a code of optimal
length is NP-hard. In this paper, we propose a deterministic algorithm that we
prove achieves this upper bound, that is, in an order almost as the worst-case
optimal code length. We also establish a connection between the pliable index
coding problem and the minrank problem over a family of mixed matrices.
