Using complementation and resequencing to minimize transitions

Abstract

In (Murgai et al., 1997) the following problem was addressed: given a set of data words or messages to be transmitted over a bus such that the sequence (order) in which they are transmitted is irrelevant, determine the optimum sequence that minimizes the total number of transitions on the bus. Stan and Burleson (1994) presented the bus-invert method as a means of encoding words for reducing I/O power, in which a word may be inverted and then transmitted if doing so reduces the number of transitions. In this paper, we combine the two paradigms into one-that of sequencing words under the bus-invert scheme for the minimum transitions, i.e., words can be complemented, reordered and then transmitted. We prove that this problem DOPI-Data Ordering Problem with Inversion-is NP-complete. We present a polynomial-time approximation algorithm to solve DOPI that comes within a factor of 1.5 from the optimum. Experimental results show that, on average, the solutions generated by our algorithm were within 4.4% of the optimum, and that resequencing along with complementation leads to 34.4% reduction in switching activity.