  In this paper we study speaker linking (a.k.a.\ partitioning) given
constraints of the distribution of speaker identities over speech recordings.
Specifically, we show that the intractable partitioning problem becomes
tractable when the constraints pre-partition the data in smaller cliques with
non-overlapping speakers. The surprisingly common case where speakers in
telephone conversations are known, but the assignment of channels to identities
is unspecified, is treated in a Bayesian way. We show that for the Dutch CGN
database, where this channel assignment task is at hand, a lightweight speaker
recognition system can quite effectively solve the channel assignment problem,
with 93% of the cliques solved. We further show that the posterior distribution
over channel assignment configurations is well calibrated.
