### Table 2. Normalized Running Time of the Four Methodsa

2006

"... In PAGE 6: ...Table2 for the normalized running time on examples of three small molecules and two proteins.) 5.... ..."

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### Table II lists the results of optimization and the run-time for ten different P/G networks. The type of network (power (P) or ground (G)) is listed for each circuit, along with the total number of nodes ( total ) and the number of user-specified critical nodes ( crt ). The results for two voltage constraint

### Table 3: Computational results with LOP Even if the solution of the LP-relaxation is found in reasonable time, the solution of the MIP remains di cult. Due to the large number of fractional variables fl in the optimal 7

### Table 4. Performance comparison with Auction on Geometric Cost Assignment Problems(AGM) terms of the number of nodes in each partition. The mean and standard devia- tion of cpu times are shown in the table, along with the speedup. The mean and standard deviation are computed using a sample size of three runs with di erent seeds for the random numbers (See Appendix A). The speedup is the ratio of the means of auction running time to ADP/A running time. For this class of problems ADP/A is seen to be one to two orders of magnitude faster than the

"... In PAGE 12: ...lgorithms. Therefore we do not report on this problem class in this paper. Now we will describe the computational results. Table4 summarizes the re- sults for the AGM problem class. The rst column indicates the problem size in... In PAGE 16: ...g., for the Assign-Geometric prob- lem class, the speedup of ADP/A increases with problem size ( Table4 ) and for the Assign-Low-Cost problem class the speedup of auction over ADP/A steadily decreases with increase in problem size (Table 8). 6.... ..."

### Table 1 Run times.

"... In PAGE 16: ... 2 10.4 Timing Comparisons Table1 lists the run times of the five programs on the various surfaces, all normalized to the run time of the Toth version A2 program (the version most consistent with the method described by Toth). Except for surface 5, where version B is slightly faster and surface 7, where version B is slightly slower, the run times of the different versions of the Toth program are the same.... ..."

### Table 3: Running Times

"... In PAGE 8: ...0% 101.0% Table3 : Running Times Time in Seconds % Improvement Tail Recursive Tail Recursive (optimized) Hand Optimized Tail Recursive (optimized) Hand Optimized insert .294 .... ..."

### Table 1: Run times

"... In PAGE 7: ... With no theoretic bound on run time, empirical results are significant. Table1 summarises simulated results. A step is a single high-level language instruction.... ..."

### Table 1 Run times.

"... In PAGE 16: ... 2 11.4 Timing Comparisons Table1 lists the run times of the flve programs on the various surfaces, all normalized to the run time of the Toth version A2 program (the version most consistent with the method described by Toth). Except for surface 5, where version B is slightly faster and surface 7, where version B is slightly... ..."

### Table 4. Run times

2002

"... In PAGE 4: ... Thus up to 2000 partitions have to be computed. The final results and the corresponding run times are given in Table 3 and Table4 , respectively. In the first three rows the results for hMETIS using 4, 5, and 10 runs per recursive split are reported.... ..."

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