Space-planning: placement of modules with controlled empty area by single-sequence

The single-sequence (simply SS ) is a permutation of integers 1,2,3,..., n each represents an object placed on a plane without mutual overlapping. An SS represents a system of ABLR-relations (above, below, left-of, right-of) between every pair of integers by SS-to-ABLR rule: if (x, y) is in SS in this order and xy, then x is left-of or below y, respectively. If objects are rooms of a T-junction floorplan of n rooms and integers denote their Abe-orders, the ABLR-relations between rooms are coded to an SS by just reading the rooms in a dual way. We enhance the definition and the fact to the case when the floorplan consists of m(≥n) rooms and the ABLR-relations are defined on the focused n of these rooms. Coding, i.e. getting the minimum SS from a given floorplan and decoding, i.e. getting the minimum floorplan from a given SS such that focused n rooms satisfy the ABLR-relations defined through the SS-to-ABLR rule are fixed by linear time algorithms. The first application is in a core technique space-planning in physical design of large systems. It is to suggest global routes to insert empty-rooms to relieve spot congestion, critical-path, crosstalk, unroutable nets, etc. without changing the ABLR-relations among the focused rooms.