  Determinization of B\"uchi automata is a long-known difficult problem and
after the seminal result of Safra, who developed the first asymptotically
optimal construction from B\"uchi into Rabin automata, much work went into
improving, simplifying or avoiding Safra's construction. A different, less
known determinization construction was derived by Muller and Schupp and appears
to be unrelated to Safra's construction on the first sight. In this paper we
propose a new meta-construction from nondeterministic B\"uchi to deterministic
parity automata which strictly subsumes both the construction of Safra and the
construction of Muller and Schupp. It is based on a correspondence between
structures that are encoded in the macrostates of the determinization
procedures - Safra trees on one hand, and levels of the split-tree, which
underlies the Muller and Schupp construction, on the other. Our construction
allows for combining the mentioned constructions and opens up new directions
for the development of heuristics.
