Arbitrary rectilinear block packing based on sequence pair

Based on the sequence pair structure, this paper proposes a novel method to represent arbitrary shaped rectilinear blocks. The necessary and sufficient conditions are derived such that non-overlapped packing of arbitrary rectilinear blocks can always be guaranteed regardless of the dimensions of the blocks. A stochastic search is applied, three sequence pair operations are defined to search the feasible solution space both continuously and exhaustively. Theoretical results derived in this paper show that an optimal solution can always be reachable through finite steps of the stochastic search. As such, the algorithm becomes a significant breakthrough in the general packing problem both theoretically and practically.

[1]  Ronald L. Rivest,et al.  Orthogonal Packings in Two Dimensions , 1980, SIAM J. Comput..

[2]  Ralph H. J. M. Otten,et al.  Automatic Floorplan Design , 1982, 19th Design Automation Conference.

[3]  Robert W. Dutton,et al.  An Analytical Algorithm for Placement of Arbitrarily Sized Rectangular Blocks , 1985, 22nd ACM/IEEE Design Automation Conference.

[4]  Martin D. F. Wong,et al.  A New Algorithm for Floorplan Design , 1986, 23rd ACM/IEEE Design Automation Conference.

[5]  Uri M. Ascher,et al.  Model and solution strategy for placement of rectangular blocks in the Euclidean plane , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[6]  Wayne Wei-Ming Dai,et al.  Hierarchical placement and floorplanning in BEAR , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[7]  Ting-Chi Wang,et al.  An optimal algorithm for floorplan area optimization , 1990, 27th ACM/IEEE Design Automation Conference.

[8]  Ting-Chi Wang,et al.  A graph theoretic technique to speed up floorplan area optimization , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[9]  Tsu-Chang Lee,et al.  A Bounded 2D Contour Searching Algorithm for Floorplan Design with Arbitrarily Shaped Rectilinear and Soft Modules , 1993, 30th ACM/IEEE Design Automation Conference.

[10]  Yoji Kajitani,et al.  Rectangle-packing-based module placement , 1995, ICCAD.

[11]  Yoji Kajitani,et al.  Module placement on BSG-structure and IC layout applications , 1996, ICCAD 1996.

[12]  Wayne Wei-Ming Dai,et al.  General floorplanning with L-shaped, T-shaped and soft blocks based on bounded slicing grid structure , 1997, Proceedings of ASP-DAC '97: Asia and South Pacific Design Automation Conference.

[13]  Wayne Wei-Ming Dai,et al.  Topology constrained rectilinear block packing for layout reuse , 1998, ISPD '98.

[14]  Floorplanning for deep submicron vlsi design , 1998 .

[15]  Jin Xu,et al.  Rectilinear block placement using sequence-pair , 1998, ISPD '98.

[16]  Yoji Kajitani,et al.  Module placement on BSG-structure with pre-placed modules and rectilinear modules , 1998, Proceedings of 1998 Asia and South Pacific Design Automation Conference.