Floorplanning

Non-Slicing Floorplan Representation Rectangle-Packing-Based Module Placement, H. Murata, K. Fujiyoushi, S. Nakatake and Y. Kajitani, IEEE International Conference on Computer-Aided Design, 1995, pages Rectangle-Packing-Based Module Placement, H. Murata, K. Fujiyoushi, S. Nakatake and Y. Kajitani, IEEE International Conference on Computer-Aided Design, 1995, pages

Sequence Pair (SP) A floorplan is represented by a pair of permutations of the module names: e.g A sequence pair (s 1, s 2 ) of n modules can represent all possible floorplans formed by the n modules by specifying the pair-wise relationship between the modules.

Sequence Pair Consider a pair of modules A and B. If the arrangement of A and B in s 1 and s 2 are: –(…A…B…, …A…B…), then the right boundary of A is on the left hand side of the left boundary of B. –(…A…B…, …B…A…), then the upper boundary of B is below the lower boundary of A.

Example Consider the sequence pair: (13245,41352 ) Any other SP that is also valid for this packing?

Floorplan Realization Floorplan realization is the step to construct a floorplan from its representation. How to construct a floorplan from a sequence pair? We can make use of the horizontal and vertical constraint graphs (G h and G v ).

Floorplan Realization Whenever we see (…A…B…, …A…B…), add an edge from A to B in G h with weight w A. Whenever we see (…A…B…, …B…A…), add an edge from B to A in G v with weight h A. Add a source vertex s to G h and G v pointing, with weight 0, to all vertices without incoming edges. Finally, find the longest paths from s to every vertex in G h and G v (how?), which are the coordinates of the lower left corner of the module in the packing.

Example (13245,41352 ) s 0 0 GhGh s 0 0 GvGv

Constraint Graphs How many edges are there in G h and G v in total? Is there any transitive edges in G h and G v ? How to remove the transitive edges? Can we reduce the size of G h and G v to linear, i.e., no. of edges is of order O(n), by removing all the transitive edges?

Moves Three kinds of moves in the annealing process: M1: Rotate a module, or change the shape of a module M2: Interchange 2 modules in both sequences M3: Interchange 2 modules in the first sequence Does this set of move operations ensure reachability? Why?

Pros and Cons of SP Advantages: –Simple representation –All floorplans can be represented. –The solution space is finite. (How big?) Disadvantages: –Redundant representation. The representation is not 1-to-1. –The size of the constraint graphs, and thus the runtime to construct the floorplan, is quadratic.

Questions Is the SP representation for general non- slicing floorplan P-admissible? Can we improve the runtime to realize a floorplan from its SP representation? (FAST-SP: A Fast Algorithm for Block Placement on Sequence Pair, X. Tang and D.F. Wong, ASP-DAC 2001, pp )

Mosaic Floorplan Representation Revisiting Floorplan Representations, B. Yao, H. Chen, C.K. Cheng and R. Graham, International Symposium on Physical Design, 2001, pages Revisiting Floorplan Representations, B. Yao, H. Chen, C.K. Cheng and R. Graham, International Symposium on Physical Design, 2001, pages

Mosaic Floorplan A mosaic packing can be represented by a pair of twin binary trees: A B C D E F C AF D E B T1T1 B AE D C F T2T2

Twin Binary Trees An arbitrary pair of trees may not correspond to a valid packing. They must be twin binary to each other, i.e., their labelings are complement of each other.

Labeling The labeling of a tree T can be obtained by traversing the tree in in-order and append a bit 0 (1) to the labeling if a node, except the leftmost (rightmost) node, with no left (right) child is visited: C AB D C AB D Labeling of T = 101 T

Twin Binary Trees A B C D E F C AF D E B T1T1 B AE D C F T2T Labeling of T 1 = Labeling of T 2 = 01100

Floorplan Representations Slicing Floorplan: –A New Algorithm for Floorplan Design, DAC 1986, pp Mosaic Floorplan: –Corner Block List: An Effective and Efficient Topological Representation of Non-slicing Floorplan, ICCAD 2000, pp –The Quarter-State Sequence (Q-sequence) to Represent the Floorplan and Applications to Layout Optimization, ASP-DAC 2000, pp –Revisiting Floorplan Representations, ISPD 2001, pp

Floorplan Representations Non-slicing Floorplan: –Rectangle-Packing-Based Module Placement, ICCAD 1995, pp –Module Placement on BSG-structure and IC Layout Applications, ICCAD 1996, pp –An O-tree Representation of Non-slicing Floorplan and its Applications, DAC 1999, pp –B*-tree: A New Representation for Non-slicing Floorplans, DAC 2000, pp –TCG: A Transitive Closure Graph-based Representation for Non- slicing Floorplans, DAC 2001, pp –Twin Binary Sequences: A Non-redundant Representation for General Non-slicing Floorplan, ISPD 2002, pp