Acknowledgments We Have Enjoyed Research Discussions With

Table 1: Scaled Cost values (10 5) of best k-way partitions obtained using d-dimensional embed-dings, 1 d 10. Results for KP and EIG1 are quoted from 4], and results for KC are quoted from 2]. References 1] C. for uniformly random pointsets, illustrating the exi-bility of the DP-RP approach 1].] Figure 5 describes Cluster Costs for f corresponding to Scaled Cost; the procedure returns all cluster costs w(C i;j]) in O(nU) time, assuming O(n) signal nets. This is a valid assumption since both fanout and cell I/O are bounded for any given technology. Steps 1-9 calculate the outdegree for each cluster, and w(C i;j]) is computed in Step 10. Given the value of w(C i;j?1]), one can compute w(C i;j]) by adding v j to cluster C i;j?1] and checking whether any cut nets become completely contained in the cluster (Step 8), or whether any previously uncut nets become cut (Step 9). Appropriate data structures allow Steps 8 and 9 to be executed in constant time, hence Cluster Costs has O(nU) time complexity 1].