Theory of T-junction floorplans in terms of single-sequence

In a placement, two rectangles on a plane are non-overlapping if and only if the relationship between them is one of ABLR (above, below, left-of, right-of)-relations. From the standpoint that a system of ABLR-relations is specified by the designer to confine the placement, the first concern is its consistency, i.e. if there is a corresponding placement. The second is an efficient way to construct a corresponding placement. The third is a handy coding of the ABLR-system all the way. In this paper, the first concern is solved by an existence condition of the primal-and dual-orders of rectangles. The second is answered by a linear time construction algorithm of a T-junction floorplan. This is new in its speed and generality with respect to the number of rooms. The third is by a new coding single-sequence SS. Its unique suitability to handle the T-junction floorplan is remarkable. Using the merit that SS can control the distribution of empty rooms, a novel application is suggested to space-planning, a recent trend in VLSI physical design to budget the space for congestion relief and interference separation (though the detail is not contained here for the space).