On approximation algorithms for microcode bit minimization

  • Authors:
  • S. S. Ravi;D. Gu

  • Affiliations:
  • Department of Computer Science, SUNY at Albany, Albany, NY;Department of Computer Science, SUNY at Albany, Albany, NY

  • Venue:
  • MICRO 21 Proceedings of the 21st annual workshop on Microprogramming and microarchitecture
  • Year:
  • 1988

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Abstract

The bit (or width) minimization problem for microprograms is known to be NP-complete. Motivated by its practical importance, we address the question of obtaining near-optimal solutions. Two main results are presented. First, we establish a tight bound on the quality of solutions produced by algorithms which minimize the number of compatibility classes. Second, we show that the bit minimization problem has a polynomial time relative approximation algorithm only if the vertex coloring problem for graphs with n nodes can be approximated to within a factor of &Ogr;(logn) in polynomial time.