  A rectangular dual of a graph $G$ is a contact representation of $G$ by
axis-aligned rectangles such that (i) no four rectangles share a point and (ii)
the union of all rectangles is a rectangle. The partial representation
extension problem for rectangular duals asks whether a given partial
rectangular dual can be extended to a rectangular dual, that is, whether there
exists a rectangular dual where some vertices are represented by prescribed
rectangles. Combinatorially, a rectangular dual can be described by a regular
edge labeling (REL), which determines the orientations of the rectangle
contacts. We characterize the RELs that admit an extension, which leads to a
linear-time testing algorithm. In the affirmative, we can construct an
extension in linear time.
