A subdivision of a rectangle into rectangular faces with horizontal and vertical line segments is called a rectangular drawing or floorplan. It has been an open problem to determine whether there exist a polynomial time algorithm for computing R(n). We affirmatively solve the problem, that is, we introduce an O(n4)-time and O(n3)-space algorithm for R(n). The algorithm is based on a recurrence for R(n), which is the main result of the paper. We also implement our algorithm and computed R(n) for n 3000.

In mobile communication systems using Dynamic Channel Assignment, channels are possible to be rearranged so that blocking probability can be made low. The smaller the number of cells where channels are rearranged, the smaller the load on the base stations in the cells. Also, we can reduce the deterioration of communication quality caused by reassingning a new channel to a call instead of the channel already assigned. In this paper, we consider not only how to rearrange channels but also which channel should be rearranged and assigned to a new call in rearrangement, and propose very simple but effective methods for rearrangement. The ways to select a candidate channel to be rearranged and assigned to a new call in the new methods make the number of cells where a channel is rearranged smaller. We also examine the relations between characteristics and the number of cells where a channel is rearranged. Using computer simulation results, the properties of the new rearrangement methods are compared with those of the traditional methods.

A floorplan is a subdivision of a rectangle into rectangular faces with horizontal and vertical line segments. Heuristic search algorithms are used to find desired floorplans in applications, including sheet-cutting, scheduling, and VLSI layout design. Representation of floorplan is critical in floorplan algorithms, because it determines the solution space searched by floorplan algorithms. In this paper, we show a surjective mapping from permutations to room-to-room floorplans. This mapping gives us a simple representation of room-to-room floorplans.

A floorplan is a subdivision of a rectangle into rectangular faces with horizontal and vertical line segments. We call a floorplan room-to-room when adjacencies between rooms are considered. Fujimaki and Takahashi showed that any room-to-room floorplan can be represented as a permutation. In this paper, we give an O(n)-time algorithm that constructs the vertical and the horizontal constraint graphs of a floorplan for a given permutation under this representation.

A polyomino is a configuration composed of squares connected by sharing edges. A k-coloring of a polyomino is an assignment of k colors to the squares of the polyomino in such a way no two adjacent squares receive the same color. A k-coloring is called balanced if the difference of the number of squares in color i and that of squares in color j is at most one for any two colors i and j. In this paper, we show that any polyomino has balanced k-coloring for k3.

The 3-D channel routing is a fundamental problem on the physical design of 3-D integrated circuits. The 3-D channel is a 3-D grid G and the terminals are vertices of G located in the top and bottom layers. A net is a set of terminals to be connected. The objective of the 3-D channel routing problem is to connect the terminals in each net with a Steiner tree (wire) in G using as few layers as possible and as short wires as possible in such a way that wires for distinct nets are disjoint. This paper shows that the problem is intractable. We also show that a sparse set of ν 2-terminal nets can be routed in a 3-D channel with O(√ν) layers using wires of length O(√ν).