The single-sequence (SS) debuted very recently as the literally simplest code to represent the consistent ABLR-relations (above, below, left-of, right-of) between every pair of objects. It is evolutional in several senses in that it does not convey the labels of objects and that objects could be either physical modules or topological rooms of a T-junction floorplan. Rather it is considered an extremal abstraction of those BSG, SP, O-Tree, etc. algorithms (for packing) and Q-seq, CBL, HPG, etc. (for floorplanning). The paper reports a discovery of a particular relation between SS and the normalized configuration of the floorplan called the unit-diagonal diagram.
"Comparing with the mappings suggested recently in  and , our mapping is as efficient (has a linear time and space complexity) and at least as simple. Furthermore, the mapping algorithm can easily find the direct neighbors of every block, with performances matching that of the algorithm suggested in . "
[Show abstract][Hide abstract] ABSTRACT: A floorplan represents the relative relations between modules on an integrated circuit. Floorplans are commonly classified as slicing, mosaic, or general. Separable and Baxter permutations are classes of permutations that can be defined in terms of forbidden subsequences. It is known that the number of slicing floorplans equals the number of separable permutations and that the number of mosaic floorplans equals the number of Baxter permutations [B. Yao, H. Chen, C.K. Cheng, R.L. Graham, Floorplan representations: complexity and connections, ACM Trans. Design Automation Electron. Systems 8(1) (2003) 55–80]. We present a simple and efficient bijection between Baxter permutations and mosaic floorplans with applications to integrated circuits design. Moreover, this bijection has two additional merits: (1) It also maps between separable permutations and slicing floorplans; and (2) it suggests enumerations of mosaic floorplans according to various structural parameters.
[Show abstract][Hide abstract] ABSTRACT: The single-sequence (simply SS) is an effective and efficient representation of non-slicing floorplan, which utilizes permutation of integers 1, 2, 3<sub>hellip</sub>, n to represent sets of ABLR-relations (above, below, left-of, right-of) that hold among n objects on the plane without overlapping. For fast decoding SS code, horizontal and vertical contours (HVC) are introduced. From geometrical information kept in HVC, not only corresponding configuration of floorplan but also placement can be realized simultaneously in linear time. Example of configuration of floorplan and experimental results on MCNC benchmarks showed the promising results of our proposed algorithm.
Communications, Circuits and Systems, 2008. ICCCAS 2008. International Conference on; 06/2008
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