  We study the classic house-swapping problem of Shapley and Scarf (1974) in a
setting where agents may have "objective" indifferences, i.e., indifferences
that are shared by all agents. In other words, if any one agent is indifferent
between two houses, then all agents are indifferent between those two houses.
The most direct interpretation is the presence of multiple copies of the same
object. Our setting is a special case of the house-swapping problem with
general indifferences. We derive a simple, easily interpretable algorithm that
produces the unique strict core allocation of the house-swapping market, if it
exists. Our algorithm runs in square polynomial time, a substantial improvement
over the cubed time methods for the more general problem.
