  Union-Find (UF) and Minimum-Weight Perfect Matching (MWPM) are popular
decoder designs for surface codes. The former has significantly lower time
complexity than the latter but is considered somewhat inferior, in terms of
decoding accuracy. In this work we present an interpretation of UF decoders
that explains why UF and MWPM decoders perform closely in some cases: the UF
decoder is an approximate implementation of the blossom algorithm used for
MWPM. This interpretation allows a generalization of UF decoders for weighted
decoding graphs and explains why UF decoders achieve high accuracy for certain
surface codes.
