Optimizations. The e cient protocol can be optimized. For simplicity the protocol was described in a way that (except for the dealer) every message that is distributed, must be distributed to every player. In fact this is not necessary. If a player p must distribute a value treep( ) of his IG-tree then it su ces that he distributes this value only to those players that are not corresponding to or any of its predecessor nodes. In other words, the IG-tree of a player p will contain no node = p with > 0. The e cient protocol can further be optimized by analyzing the concrete structure of the given adversary set which can yield a protocol that needs less runs of the basic protocol than described above.
Optimizations. This section describes in detail several compiler optimizations that had a strong impact on the pricing algorithm, and that we believe are likely to prove effective in a general context. Sec- tions 3.2 and 3.3 describe optimizations and trade-offs related to exploiting coarse-grained parallelism and strength-reduction in- variants. These are high-level transformations demonstrated using functional code snippets. Sections 3.4 and 3.5 present lower-level optimizations, related to branch divergence and memory coalesc- ing, that are demonstrated on a Fortran intermediate representation.
