3 Benchmark Method Pure Fm 2nd-level Gain 3rd-level Gain 4th-level Gain

A linear time heuristic for improving network partitions. 10] A. G. Hooman. The dynamic locking heuristic { a new graph partitioning algorithm. In Proc. 14 Krishnamurthy gain vector; this reopens the question of interpreting such seminal works in the literature as 16] and 13], whose studies used random bucket selection. Organizing the gain buckets as LIFO (Last-In-First-Out) stacks leads to a 35% improvement versus random bucket organization and a 42% improvement versus FIFO (First-In-First-Out) queues. We have also presented an alternative higher-level gain formulation, based on Krishnamurthy's approach, which incorporates some of the intuition behind the LIFO organization. This alternative formulation results in a further 16% reduction in the average cut cost when compared directly to the Krishnamurthy formulation for higher-level gains, assuming LIFO organization for the gain buckets. We believe that a much more detailed study is necessary to better understand the eeect of \obvi-ous" choices in the FM implementation on the solution quality and runtime. Thus, our future work investigates not only further tie-breaking mechanisms, but also interesting eeects that result from the order imposed by the netlist representation and the list of free modules. 6 References 1] C. 6 The input format of a netlist is typically a function of how the other development tools represent and output the circuit, and may group related nets or modules together or far apart. This relatedness/unrelatedness will in turn be reeected within the data structures used by FM to store the netlist information. Table 6: Average cutsize results for 100 runs of our new multi-level gain formulation (columns 4-6) using LIFO, random, and FIFO organization schemes for the gain buckets. The numbers in parentheses give the minimum observed cutsizes. with higher-level gains using either random or FIFO selection. An explanation for this might be that with our new formulation, the higher-level gains are computed more carefully and tend to obviate the need for a \good" selection scheme (i.e., the results for random and FIFO will more closely mirror the results of LIFO as the length of the gain vectors increases). Also, our new formulation explicitly gives higher priority to the neighbors of moved modules, which is similar to the eeect of the LIFO selection scheme. 7 Conclusion We have shown that implementation choices play an important part for both the FM algorithm of Fiduccia and Mattheyses 8] and the algorithm of Krishnamurthy 13]. In particular, selection from gain buckets based …