### Table 1: Performance comparison on the task of automatic image annotation on the Corel dataset. CRM and CRM-Rectangles are essentially the same model but the former uses regions produced by a segmentation algorithm while the latter uses a grid. Note that using a grid improves performance. MBRM performs best beating even CRM-Rectangles by a small amount.

"... In PAGE 6: ... To evaluate the system performance, recall and precision values are averaged over the testing words. The first set of results are shown for the Corel dataset in Table1 . Results are reported for all (260) words in the test set.... ..."

### Table 1: Data from enumeration of reduced k n rectangles. 19

1999

"... In PAGE 18: ... Results for small squares The theoretical results given to date have dealt with the distribution of intercalates in large rectangles. As a counterpoint, in Table1 we display the results of a computer enumeration of small order Latin squares and rectangles; and the number of intercalates contained therein. Since intercalates survive permutations of the rows and columns it su ces to enumerate LR(k; n), the set of reduced k n Latin rectangles.... In PAGE 18: ... On the basis of Theorem 2 we might expect this value to be close to k. The actual values (to 4 decimal places) can be found in Table1 . We are also interested in the proportion of Latin rectangles which contain no intercalates, namely jS0j jL(k; n)j.... In PAGE 18: ... We are also interested in the proportion of Latin rectangles which contain no intercalates, namely jS0j jL(k; n)j. Theorem 1 suggests that this ratio will be approximately e? k, which is to say that the values in the nal column of Table1 should also be close to k. Since much attention has focused on N2 squares we provide separate counts of them in Table 2.... ..."

Cited by 3

### Table 3. Classi cation of Areas in Lemma 3 3. EXTENSION In the previous analyses, we require the shape exibility r to be at least two. This is justi ed by our assumption that each rectangle has a considerable amount of exibility in its shape. In this section, we modify the packing technique slightly to accommodate the case when r = 2 ? where is a small positive number. We are able to obtain a similar result as before. Due to the limitation in space, we will not show the proof here. Theorem 2 Given a set of soft rectangles of total area Atotal, maximum area Amax and shape exibility r = 2 ? where is a small positive number, there exists a slicing oorplan F such that

1997

"... In PAGE 5: ... The areas are again classi ed into groups. The areas, the widths and the heights of di erent groups are shown in Table3 . We use a similar packing technique as before.... ..."

Cited by 11

### Table 2: Relative Speed-ups for Orthogonal Range Queries hot spot distribution HS(500)

1994

"... In PAGE 10: ....1.2. Orthogonal Range Queries Table2 shows the performance of the alternative disk allocation function for orthogonal range queries. The queries include small rectangles (BSR(H,W), and BSR(N,N)), and all rectangles, columns and rows of the coordinate space [0.... ..."

Cited by 17

### Table 5: Parallel Run-time for Orthogonal Range Queries hot spot distribution HS(500)

1995

"... In PAGE 13: ....1.2. Orthogonal Range Queries Table5 shows the performance of the alternative disk allocation function for orthogonal range queries. The queries include small rectangles (BSR(H,W) and BSR(N,N)), and all rectangles, columns and rows of the coordinate space [0.... ..."

Cited by 5

### TABLE 7. Computational results for Set I 38 small problems taken from the literature. Part 1 of 3: problem classes ngcut and hccut. For each instance, the table lists: its dimension (W H); m, the number of types of rectangles to pack; M, the maximum number of rectangles that can be packed; the optimal or best known solution (BKS); and solutions found by algorithms PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH, as well as the average solution time for HH in seconds. Entries in boldface indicate best known value or better was obtained.

### TABLE 8. Computational results for Set I 38 small problems taken from the literature. Part 2 of 3: problem classes okp and cgcut. For each instance, the table lists: its dimension (W H); m, the number of types of rectangles to pack; M, the maximum number of rectangles that can be packed; the optimal or best known solution (BKS); and solutions found by algorithms PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH, as well as the average solution time for HH in seconds. Entries in boldface indicate best known value or better was obtained.

### TABLE 9. Computational results for Set I 38 small problems taken from the literature. Part 3 of 3: problem classes gcut and wang. For each instance, the table lists: its dimension (W H); m, the number of types of rectangles to pack; M, the maximum number of rectangles that can be packed; the optimal or best known solution (BKS); and solutions found by algorithms PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH, as well as the average solution time for HH in seconds. Entries in boldface indicate best known value or better was obtained.

### Table 2: Cost comparisons of BpR, BLSD and BSA for 2000 points, resp. rectangles, and cb = 16.

1995

"... In PAGE 7: ...0 and consider a larger part of the regional bench- mark (also about 2000 objects). Table2 shows the per- formance results for bucket capacity cb = 16. 6 Taking External Directory Accesses Into Account Although the time penalty incured by external directory page accesses is small compared to data bucket accesses, it would be desirable (at least from a theoretical viewpoint) to extend the performance measure and the optimization e orts to cover external directory page accesses as well.... ..."

Cited by 14

### Table 1: Parameters for the rectangle generator

"... In PAGE 3: ...1 The Rectangle Generator At the Ecole Nationale Sup erieure des T el ecommunications (ENST) we have implemented a tool to generate sets of rectangles with edges parallel to the axes. Users can specify the parameters listed in Table1 . For the rst ve parameters, the user has to specify some statistical distribution with the usual parameters.... ..."