  We consider swapping of two records in a microdata set for the purpose of
disclosure control. We give some necessary and sufficient conditions that some
observations can be swapped between two records under the restriction that a
given set of marginals are fixed. We also give an algorithm to find another
record for swapping if one wants to swap out some observations from a
particular record. Our result has a close connection to the construction of
Markov bases for contingency tables with given marginals.
