Wirelength Optimal Rectangle Packings
نویسندگان
چکیده
Finding wirelength optimal packings of rectangles is a well known problem in VLSI design. We propose a branch and bound algorithm for this problem that is based on the rectangle packing algorithm of Moffitt and Pollack. It makes use of a very efficient implementation of an incremental network simplex algorithm. Our algorithm allows for the first time to find optimum solutions of three instances of the well known MCNC block packing benchmark and optimally solves real-world instances with up to 15 rectangles in 1 hour. The largest instance so far for which an optimum solution has been computed contained 6 blocks.
منابع مشابه
An exact algorithm for wirelength optimal placements in VLSI design
We present a new algorithm designed to solve floorplanning problems optimally. More precisely, the algorithm finds solutions to rectangle packing problems which globally minimize wirelength and avoid given sets of blocked regions. We present the first optimal floorplans for 3 of the 5 intensely studied MCNC block packing instances and a significantly larger industrial instance with 27 rectangle...
متن کاملAnchored Rectangle and Square Packings
For points p1, . . . , pn in the unit square [0, 1] , an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles r1, . . . , rn ⊆ [0, 1] such that point pi is a corner of the rectangle ri (that is, ri is anchored at pi) for i = 1, . . . , n. We show that for every set of n points in [0, 1], there is an anchored rectangle packing of area at least 7/12 − O(1/n), and...
متن کاملCircular wirelength of Generalized Petersen Graphs
In this paper we formulate the Vertex Congestion Lemma leading to a new technique in computing the exact wirelength of an embedding. We compute the circular wirelength of generalized Petersen graphs by partitioning the vertices as well as the edges of cycles. Further we obtain the linear wirelength of circular ladders. Our algorithms produce optimal values in linear time.
متن کامل0 Compactness Theorems for Geometric Packings
Moser asked whether the collection of rectangles of dimensions 1 × 1 4 ,. .. , whose total area equals 1, can be packed into the unit square without overlap, and whether the collection of squares of side lengths 1 4 ,. .. can be packed without overlap into a rectangle of area π 2 6 − 1. Computational investigations have been made into packing these collections into squares of side length 1 + ε ...
متن کاملPenny-Packings with Minimal Second Moments
We consider the problem of packing n disks of unit diameter in the plane so as to minimize the second moment about their centroid. Our main result is an algorithm which constructs packings that are optimal among hexagonal packings. Using the algorithm, we prove that, except for n = 212, the n-point packings obtained by Graham and Sloane [1] are optimal among hexagonal packings. We also prove a ...
متن کامل