In this paper, we investigate how one can modify an orthogonal graph drawing to accommodate the placement of overlap-free labels with the minimum cost (i.e., minimum increase of the area and preservation of the quality of the drawing). We investigate computational complexity issues of variations of that problem, and we present polynomial time algorithms that find the minimum increase of space in one direction, needed to resolve overlaps, while preserving the orthogonal representation of the orthogonal drawing when objects have a predefined partial order.
