Enumerating Floorplans with n Rooms
نویسنده
چکیده
A plane drawing of a graph is called a floorplan if every face (including the outer face) is a rectangle. A based floorplan is a floorplan with a designated base line segment on the outer face. In this paper we give a simple algorithm to generate all based floorplans with at most n faces. The algorithm uses O(n) space and generates such floorplans in O(1) time per floorplan without duplications. The algorithm does not output entire floorplans but the difference from the previous floorplan. By modifying the algorithm we can generate without duplications all based floorplans having exactly n faces in O(1) time per floorplan. Also we can generate without duplications all (non-based) floorplans having exactly n faces in O(n) time per floorplan. key words: graphs algorithms, plane graphs, plane trees, enu-
منابع مشابه
A Study on Hierarchical Floorplans of Order k
A floorplan is a rectangular dissection which describes the relative placement of electronic modules on the chip. It is called a mosaic floorplan if there are no empty rooms or cross junctions in the rectangular dissection. We study a subclass of mosaic floorplans called hierarchical floorplans of order k (abbreviated HFOk). A floorplan is a hierarchical floorplan of order k if it can be obtain...
متن کاملOptimal Binary Representation of Mosaic Floorplans and Baxter Permutations
A floorplan is a rectangle subdivided into smaller rectangular blocks by horizontal and vertical line segments. Two floorplans are considered equivalent if and only if there is a bijection between the blocks in the two floorplans such that the corresponding blocks have the same horizontal and vertical boundaries. Mosaic floorplans use the same objects as floorplans but use an alternative defini...
متن کاملA simple optimal binary representation of mosaic floorplans and Baxter permutations
A floorplan is a rectangle subdivided into smaller rectangular sections by horizontal and vertical line segments. Each section in the floorplan is called a block. Two floorplans are considered equivalent if and only if there is a one-to-one correspondence between the blocks in the two floorplans such that the relative position relationship of the blocks in one floorplan is the same as the relat...
متن کاملThe Quarter-State-Sequence Floorplan Representation
A floorplan of a bounding box is its dissection into rectangles (rooms) by horizontal and vertical segments. This paper proposes a string data structure called the Quarter-state sequence (or Q sequence) to represent the floorplan. The Q sequence is a concatenation of the states of rooms along the Abe order and is related to the VH graph, which is the union of the vertical-constraint and horizon...
متن کاملExploiting Air-Pressure to Map Floorplans on Point Sets
We prove a conjecture of Ackerman, Barequet and Pinter. Every floorplan with n internal segments can be embedded on every set of n points in generic position. The construction makes use of area universal floorplans also known as area universal rectangular layouts. The notion of area used in our context depends on a non-uniform density function. We, therefore, have to generalize the theory of ar...
متن کامل