Stochastic Models for Wireability Analysis of Gate Arrays

Average Interconnection Length and Interconnection Distribution for Rectangular Arrays

“…In this section we utilize the approach outlined by Sastry and Parker [6,7] to characterize intercon nection length distributions. Our analysis differs in that we distinguish between different placement stra tegies which result in one-and two-dimensional array representations.…”

“…The terminal-block relationship, T=aBp , Rent's rule, where a and p are empirical constants and p is typically between .57 and .75 [3] has proved useful in the analysis of interconnection lengths [4][5][6][7][8][9][10][11]. The Rent relationship provides a measure of the number of interconnections which cross a given boundary which encloses B blocks.…”

“…We generalize the Rent relationship to the power-law relationship, aZ?P, where p is referred to as the partitioning coefficient, and investigate the use of the power-law relationship in a number of studies [4][5][6][7]11]. Based on these investigations we determine whether there is a one-to-one correspondence between p , the empirical coefficient of the Rent relationship, and p, the partitioning coefficient of the power-law relationship.…”

“…In section 2 we consider the methodology presented by Sastry and Parker [6,7] in describing inter connection distributions based on Rent's rule. We expand their analysis to a two-dimensional lattice model and introduce the notion of separate partitioning coefficients for one-and two-dimensional placements of logic cells.…”

On routing demand and congestion estimation for FPGAs

“…Wei [7] used Rent's rule and arrived on a statistical model for hierarchical FPGA routing prediction. Some other works that indirectly address the routing resource prediction or evaluation include the congestion minimization techniques due to Wang and Sarrafzadeh [15], simultaneous place and route by Nag and Rutenbar [11], and wireability analysis for gate arrays by Sastry and Parker [13].…”