  Partial clique covering is one of the most basic coding schemes for index
coding problems, generalizing clique and cycle covering on the side information
digraph and further reducing the achievable broadcast rate. In this paper, we
start with partition multicast, a special case of partial clique covering with
cover number 1, and show that partition multicast achieves the optimal
broadcast rate of the multiple-unicast index coding if and only if the side
information digraph is partially acyclic. A digraph is said to be partially
acyclic if its sub-digraph induced by the vertex with maximum in-degree and its
incoming neighbors in the complementary digraph is acyclic. We further extend
to the general partial clique covering, offering sufficient conditions of its
optimality and sub-optimality with the aid of strong connectivity
decomposition. In addition, for some digraph classes, we also prove that the
optimal broadcast rate can be approximated by partial clique covering (as well
as by other basic schemes) within either a constant factor, or a multiplicative
factor of $O(\frac{n}{\log n})$, or $O(n^\epsilon)$ for some $\epsilon \in
(0,1)$.
