  Consider a finite set of sources, each producing i.i.d. observations that
follow a unique probability distribution on a finite alphabet. We study the
problem of matching a finite set of observed sequences to the set of sources
under the constraint that the observed sequences are produced by distinct
sources. In general, the number of sequences $N$ may be different from the
number of sources $M$, and only some $K \leq \min\{M,N\}$ of the observed
sequences may be produced by a source from the set of sources of interest. We
consider two versions of the problem -- one in which the probability laws of
the sources are known, and another in which the probability laws of the sources
are unspecified but one training sequence from each of the sources is
available. We show that both these problems can be solved using a sequence of
tests that are allowed to produce "no-match" decisions. The tests ensure
exponential decay of the probabilities of incorrect matching as the sequence
lengths increase, and minimize the "no-match" decisions. Both tests can be
implemented using variants of the minimum weight matching algorithm applied to
a weighted bipartite graph. We also compare the performances obtained by using
these tests with those obtained by using tests that do not take into account
the constraint that the sequences are produced by distinct sources. For the
version of the problem in which the probability laws of the sources are known,
we compute the rejection exponents and error exponents of the tests and show
that tests that make use of the constraint have better exponents than tests
that do not make use of this information.
