### Table 1 Amortized run times are represented with a apos;* apos; all other run times are worst-case.

### Table 2: Amortized processing times (hypercube) Fat-tree, multiple queries Binary tree, single query

"... In PAGE 10: ... In this way (for more details, see Appendix A and [5]), we get a reliable platform for a fair experimental comparison between the multiple query algorithm and the binary{tree single{query algorithm, as well as for a fair comparison between the two versions of our multiple query algorithm based on the hypercube and fat{tree topology respectively. Speci cally, in the rst table16 ( Table2 ), the amortized processing times (Rp, in seconds) as well as the corresponding achieved utilization values (Up17, in percent values) are presented, for both the hypercube{ based multiple{query algorithm and the binary{tree single{query algorithm. We present measurements for varying number of processors (16, 32, 64, 128) and for varying collection size (1/4{WSJ, 1/2{WSJ and full WSJ collection, by appropriately dividing the total number { almost 75000 { of the WSJ documents).... ..."

### Table 3: Amortized time complexity of DynamicList structure T1 T2 T3 Enqueue O(log(n)) O(1) O(1)

"... In PAGE 5: ... The tree-like structure ensures that each subsequent enqueue into T1 is of O(log(n)) complexity. Table3 summarizes the theoretical performance of DynamicList. Table 3: Amortized time complexity of DynamicList structure T1 T2 T3 Enqueue O(log(n)) O(1) O(1) ... ..."

### Table 1: Summary of the results. We denote the number of vertices and edges by n and m respectively. The running times for enumeration algorithms refer to amortized time per output. Chordal graphs Counting [ref.] Enumeration [ref.]

### Table 1: Statistics gathered with triangle sizes and different amortization factors using the 3D-BV algorithm (times are per primitive in microseconds).

in Dynamic Algorithms for Sorting Primitives Among Screen-Space Tiles in a Parallel Rendering System

"... In PAGE 7: ... As a result, for each set of rendering attributes, the amortization factor at which the client processing and server rendering times are balanced is different. As an ex- ample, Table1 shows results collected during an experiment with the 3D-BV algorithm tested with the Triangles applica- tion for triangles with a different 2D projected area. The first column of the table contains the 2D projected triangle area, while the second column lists the amortization factor used in the test.... In PAGE 7: ...he test with small triangles (e.g., 250 pixels). Quite simply, there is no single amortization value that provides the best performance for all 3D models. Finally, we observe that server rendering times (shown in the right-most column of Table1 ) increase significantly (by more than a factor of 2) with more conservative overlap clas- sifications. From this observation, we conclude that the ge- ometry processing required by each server to clip 3D primi- tives projecting to areas entirely outside its tile is significant, and thus calculating reasonably exact tile overlaps is impor- tant to constructing a scalable sort-first rendering system.... ..."

### Table 1: Statistics gathered with triangle sizes and different amortization factors using the 3D-BV algorithm (times are per primitive in microseconds).

in Dynamic Algorithms for Sorting Primitives Among Screen-Space Tiles in a Parallel Rendering System

"... In PAGE 7: ... As a result, for each set of rendering attributes, the amortization factor at which the client processing and server rendering times are balanced is different. As an ex- ample, Table1 shows results collected during an experiment with the 3D-BV algorithm tested with the Triangles applica- tion for triangles with a different 2D projected area. The first column of the table contains the 2D projected triangle area, while the second column lists the amortization factor used in the test.... In PAGE 7: ...he test with small triangles (e.g., 250 pixels). Quite simply, there is no single amortization value that provides the best performance for all 3D models. Finally, we observe that server rendering times (shown in the right-most column of Table1 ) increase significantly (by more than a factor of 2) with more conservative overlap clas- sifications. From this observation, we conclude that the ge- ometry processing required by each server to clip 3D primi- tives projecting to areas entirely outside its tile is significant, and thus calculating reasonably exact tile overlaps is impor- tant to constructing a scalable sort-first rendering system.... ..."

### Table 1. This time is relatively small and is generally amortized over a large number of frequency queries. If the binary trie is restricted to only those items that are frequent (level truncated trie), this time can be further reduced.

2000

"... In PAGE 9: ... Table1 : CPU time for building the trie and the level-truncated trie of transaction sets Compression Ratios from Patricia Tries. In Table 2, we present the e ect of compressing tries into Patricia tries and its e ect on query time.... ..."

Cited by 6

### Table 2: Amortized beam tracing statistics.

"... In PAGE 11: ... Process the polygon sequences to find all valid 5th- order specular reflection paths from the source point to the receiver. Table2 shows times (in seconds) measured during each test. The first column ( P ) lists the receiver point, and the second ( Box Size ) indicates the source box width in inches.... ..."

### Table 1. Execution speed: reference model vs.Turandot

"... In PAGE 2: ...Table1... In PAGE 7: ... The results indicate that the validated version of Turandot provides performance projections that are within 5% of those obtained from a detailed model, with a simu- lation speedup factor around 70. Based on the data in Table1 , we believe it is advanta- geous to have a validated fast processor model as a vehicle for design trade-off studies, even if not all the details of the processor are included in the model. The average time to execute a trace containing 100 million instructions by the reference model used is on the order of 30 hours, whereas the corresponding time for Turandot is only about 30 minutes.... ..."