The complexity of VLSI power-delay optimization by interconnect resizing
The lithography used for 32 nanometers and smaller VLSI process technologies restricts the interconnect widths and spaces to a very small set of admissible values. Until recently the sizes of interconnects were allowed to change continuously and the implied power-delay optimal tradeoff could be formulated as a convex programming problem, for which classical search algorithms are applicable. Once the admissible geometries become discrete, continuous search techniques are inappropriate and new combinatorial optimization solutions are in order. A first step towards such solutions is to study the complexity of the problem, which this paper is aiming at. Though dynamic programming has been shown lately to solve the problem, we show that it is NP-complete. Two typical VLSI design scenarios are considered. The first trades off power and sum of delays (L 1), and is shown to be NP-complete by reduction of PARTITION. The second considers power and max delays (L ∞), and is shown to be NP-complete by reduction of SUBSET_SUM.
KeywordsPower-delay optimization VLSI interconnects NP-completeness
Unable to display preview. Download preview PDF.
- Boese KD, Kahng AB, McCoy BA, Robins G (1993) Fidelity and near optimality of Elmore-based routing constructions. Digest of technical papers, ICCAD, pp 81–84 Google Scholar
- ITRS—International Technology Roadmap for Semiconductors, 2009 edn. http://www.itrs.net/Links/2009ITRS/Home2009.htm
- Magen N, Kolodny A, Weiser U, Shamir N (2004) Interconnect power dissipation in a microprocessor. In: International workshop on system-level interconnect prediction, pp 7–13 Google Scholar
- Moiseev K, Wimer S, Kolodny A (2009) Power-delay optimization in vlsi microprocessors by wire spacing. ACM Trans Des Automat Electron Syst 14(4):55 Google Scholar
- Moiseev K, Kolodny A, Wimer S (2010) Interconnect bundle sizing under discrete design rules. IEEE Trans Comput Aided Des Integr Circuits Syst 29(10) (to appear) Google Scholar
- Moore GE (1965) Cramming more components onto integrated circuits. Electronics 38(8) Google Scholar
- Weste N, Harris D (2010) CMOS VLSI design: circuit and system perspective. Addison Wesley/Longman, Reading/Harlow Google Scholar