### Table 3: Comparison of AM and Augmented Versions of LL: Assessment of di erence with AM

1997

"... In PAGE 8: ... In the data reported, LL was tested in the condition in which only the single nearest neighbour was considered. In Table3 the success score of AM is compared with the performance of LL apos;s basic scheme (LL), and the three augmentations of LL, viz. LL-IG, LL-MVDM and LL-IG-MVDM.... In PAGE 8: ...The results displayed in Table3 pertain to a training set in which no additional noise is added. When additional noise is present, the comparisons of AM and LL do not show many discrepancies: in all conditions, there are hardly any results that can be marked as signi cantly di erent.... ..."

Cited by 8

### Table 8 shows results of applying MFB augmented by approximate forcing to a version of

"... In PAGE 21: ...Strategy Traditional IS-1 IS-2 IS-3 IS-4 Point Estimate 3:3 #02 10 ,7 3:8 #02 10 ,7 3:4 #02 10 ,7 3:8 #02 10 ,7 3:5 #02 10 ,7 Relative Error 10#25 10#25 10#25 10#25 10#25 Replications 1,184,152,657 4,593,933 574,091 2,162,765 39,870 CPU Time #28sec.#29 740,699 4,871 610 2,320 128 Table8 : Results for Modi#0Ced Machine-Repairman Model... In PAGE 21: ... In the modi#0Ced model, type-one components have scale parameter #0C 1 = 30; type-two components have scale parameter #0C 2 = 15. The IS-4 strategy is shown in Table8 to be e#0Bective despite these signi#0Ccant changes to the failure distributions of components of the model. V Conclusions Traditional simulation techniques perform poorly when the desired performance measure is based on a rare event.... ..."

### Table 2: An objective function for the canonical version of YPPL. Indented terms replace or augment the terms immediately above them.

"... In PAGE 9: ... A larger amount of padding is left at the end of column 4 to ensure that the page meets its minimum-padding requirement. Once the decoding process has been applied to a candidate solution, the resulting pagina- tion and layout can be evaluated using the objective function in Table2 . This table presents the actual terms and weights used to implement the general criteria of Table 1.... In PAGE 9: ... Therefore, the terms overflow and out of section must still be included in the objective function in order to strongly disfavor very undesirable candidate solutions. But given their inclusion, the two additional terms overflow area and distance out of section introduced in Table2 may appear redundant. However, without these proportional terms, layouts with any over ow or out-of- section ads would be considered equivalent, regardless of the degree of the infraction.... In PAGE 9: ... For this reason, these two terms are added to aid in optimization of the more primitive overflow and out of section terms. The nal way in which the speci c terms of Table2 vary from the general criteria in Table 1 is in the implementation of the num pages criterion. Rather than penalizing ller merely by adding a cost proportional to the number of pages used in the layout, we treat bubble and padding costs separately.... In PAGE 15: ...Allowing 2%-6% for ller gives a range of 42-44 pages, so we ran three sets of experiments in which ads were distributed initially over 42, 43, and 44 pages, respectively (see Table 3).3 Figures 4 through 6 plot objective-function scores (using the objective function from Table2 ) against the number of iterations (one candidate solution is formulated and evaluated per iteration) for 20 runs of the algorithm, all seeded with di erent random numbers. (One million iterations of the algorithm on this data set requires approximately two hours on a DEC 3000/400 AXP workstation.... ..."

### Table 2. An objective function for the canonical version of YPPL. Indented terms replace or augment the terms immediately above them.

"... In PAGE 7: ... A larger amount of padding is left at the end of column 4 to ensure that the page meets its minimum-padding requirement. Once the decoding process has been applied to a candidate solution, the resulting pagina- tion and layout can be evaluated using the objective function in Table2 . This table presents the actual terms and weights used to implement the general criteria of Table 1.... In PAGE 9: ...329 disfavor very undesirable candidate solutions. But given their inclusion, the two additional terms OVERFLOW_AREA and DISTANCE_OUT_OF_SECTION introduced in Table2 may appear redundant. However, without these proportional terms, layouts with any overflow or out- of-section ads would be considered equivalent, regardless of the degree of the infraction.... In PAGE 9: ... For this reason, these two terms are added to aid in optimization of the more primitive OVERFLOW and OUT_OF_SECTION terms. The final way in which the specific terms of Table2 vary from the general criteria in Table 1 is in the implementation of the NUM_PAGES criterion. Rather than penalizing filler merely by adding a cost proportional to the number of pages used in the layout, we treat bubble and padding costs separately.... In PAGE 12: ... Allowing 2%-6% for filler gives a range of 42-44 pages, so we ran three sets of experiments in which ads were distributed initially over 42, 43, and 44 pages, respectively (see Table 3) 3 . Figures 4 through 6 plot objective-function scores (using the objective function from Table2 ) against the number of iterations (one candidate solution is formulated and evaluated per iteration) for 20 runs of the algorithm, all seeded with different random numbers. (One million iterations of the algorithm on this data set requires approximately two hours on a DEC 3000/400 AXP workstation.... ..."

### Table 2: Comparison of greedy MRTA, Best-Drop, and CPLEX ILP (all results are averages over 100 random instances). (a) versions use only terminals or Steiner points of T as endpoints of augmentation paths, (b) versions can use all Hanan grid vertices that are on tree edges.

"... In PAGE 5: ... The (c) version of the greedy MRTA algorithm gives almost identical results to the (b) version in experiments with 1 A0 20% wire- length budget and 5A020 terminals, and we omit its results. Table2 gives the number of augmenting paths, percentage of bicon- nected tree edges, and runtime for versions (a) and (b) of the greedy MRTA, Best-Drop, and ILP algorithms. The results show that ver- sions (b) achieve better solution quality than versions (a); for the greedy MRTA algorithm version (b) is better than version (a) by as much as 18BM54%.... ..."

### Table 2: Comparison of greedy MRTA, Best-Drop, and CPLEX ILP (all results are averages over 100 random instances). (a) versions use only terminals or Steiner points of T as endpoints of augmentation paths, (b) versions can use all Hanan grid vertices that are on tree edges.

"... In PAGE 5: ... The (c) version of the greedy MRTA algorithm gives almost identical results to the (b) version in experiments with 1 A0 20% wire- length budget and 5A020 terminals, and we omit its results. Table2 gives the number of augmenting paths, percentage of bicon- nected tree edges, and runtime for versions (a) and (b) of the greedy MRTA, Best-Drop, and ILP algorithms. The results show that ver- sions (b) achieve better solution quality than versions (a); for the greedy MRTA algorithm version (b) is better than version (a) by as much as 18BM54%.... ..."

### TABLE II COMPARISON OF GREEDY MRTA, BEST-DROP, AND CPLEX ILP (ALL RESULTS ARE AVERAGES OVER 100 RANDOM INSTANCES). (A) VERSIONS USE ONLY TERMINALS OR STEINER POINTS OF T AS ENDPOINTS OF AUGMENTATION PATHS, (B) VERSIONS CAN USE ALL HANAN GRID VERTICES THAT ARE ON TREE EDGES.

2002

Cited by 5

### TABLE II COMPARISON OF GREEDY MRTA, BEST-DROP, AND CPLEX ILP (ALL RESULTS ARE AVERAGES OVER 100 RANDOM INSTANCES). (A) VERSIONS USE ONLY TERMINALS OR STEINER POINTS OF T AS ENDPOINTS OF AUGMENTATION PATHS, (B) VERSIONS CAN USE ALL HANAN GRID VERTICES THAT ARE ON TREE EDGES.

2002

Cited by 5