  A hole in a graph is an induced cycle of length at least $4$, and an antihole
is the complement of an induced cycle of length at least $4$. A hole or
antihole is long if its length is at least $5$. For an integer $k$, the
$k$-prism is the graph consisting of two cliques of size $k$ joined by a
matching. The complexity of Maximum (Weight) Independent Set (MWIS) in
long-hole-free graphs remains an important open problem. In this paper we give
a polynomial time algorithm to solve MWIS in long-hole-free graphs with no
$k$-prism (for any fixed integer $k$), and a subexponential algorithm for MWIS
in long-hole-free graphs in general. As a special case this gives a polynomial
time algorithm to find a maximum weight clique in perfect graphs with no long
antihole, and no hole of length $6$. The algorithms use the framework of
minimal chordal completions and potential maximal cliques.
