### Table 1: Various covers for the polygon in Figure 3(a). Each en- try contains the number of polygons in the cover and the average coverage ratio of a polygon in the cover after the enlargement.

"... In PAGE 4: ... To evaluate the quality of the cover, we counted the number of polygons in the cover and calculated the size of each polygon with respect to the size of the original polygon. Table1 illustrates the results obtained using different cover strategies and different face orders for the polygon in Figure 3(a). As can be seen, in most cases, the resulting cover consists of three polygons whose average coverage ratio is 59%.... ..."

### Table 3 reports the maximum, minimum, and average number of subge- ometries in the grid rectangles, for the combination of the four layers. We also compared the sizes of the database before and after computing the sub- polygonization: the initial size of the database is 166 Mega Bytes. After the precomputation of the overlay of the four layers, the database occupies 621 Mega Bytes.

2008

"... In PAGE 41: ...ueries were evaluated over the entire map (i.e., no query region was specified). Table3 shows the queries and their expressions in the postGIS query language. For the Piet query, the SQL translation is displayed.... In PAGE 42: ...14100 seconds 2 8 hours 4 minutes 30.4810 seconds Table 2: Total sub-polygonization times Subgeometry Max Min Avg # of Carrier Lines per rectangle 616 4 15 # of Points per rectangle (carrier lines intersection in a rectangle) 107880 4 452 # of Segment Lines per rectangle (segments of carrier lines in a rectangle) 212256 4 868 # of Polygons per rectangle 104210 1 396 Table3 : Number of sub-geometries in the grid for the 4-layers overlay. generated by Piet against the PostgreSQL database.... ..."

### TABLE I THE NAMESPACE REGION CERTIFICATION TECHNIQUE IS APPLICABLE TO MOST KNOWN STRUCTURED OVERLAYS. THIS SHOWS HOW DIFFERENT SIZED REGIONS ARE SPECIFIED IN 16 POPULAR PROTOCOLS. GOSSIP PROTOCOLS CAN ONLY CERTIFY REGIONS OF A FIXED SIZE.

### Table 5. Size of the Sample of Compounds Classified to Be Active by Each Method as a Percentage of the Whole Test Set for Each Target

2005

"... In PAGE 4: ... Although the study of structure-activity relationships is not within the scope of this paper, we speculate that ligands of DH and AE contain a subset of compounds with particular features, such as steroids, which render them more easily distinguishable from the bulk of nonactives. Because, in this study, the sample size is not kept fixed but allowed to vary according to the classification, high enrichment factors can be achieved with a high number of false negatives if the sample size is small ( Table5 ). For example, TV, yielding high enrichment factors, predicts in many cases a smaller number of compounds to be active than do other methods (Table 5).... In PAGE 4: ... Because, in this study, the sample size is not kept fixed but allowed to vary according to the classification, high enrichment factors can be achieved with a high number of false negatives if the sample size is small (Table 5). For example, TV, yielding high enrichment factors, predicts in many cases a smaller number of compounds to be active than do other methods ( Table5 ). For this reason, recall values were also calculated, which give the percentage of all actives which have been retrieved (Figure 1b).... ..."

### Table 1; the preprocessing time of each data structure is O(n log n). If the query rectangles are \three-sided rectangles quot; of the form [a1; b1] [a2; 1], then one can use a priority search tree of size O(n) to answer a planar range-reporting query in time O(log n + k) [208].

1999

"... In PAGE 10: ... Table1 . Asymptotic upper bounds for planar orthogonal range searching, due to Chazelle [55, 58], in the random access machine (RAM), arithmetic pointer machine (APM), elementary pointer machine (EPM), and semigroup arithmetic models.... In PAGE 10: ... Asymptotic upper bounds for planar orthogonal range searching, due to Chazelle [55, 58], in the random access machine (RAM), arithmetic pointer machine (APM), elementary pointer machine (EPM), and semigroup arithmetic models. Each of the two-dimensional results in Table1 can be extended to queries in Rd at a cost of an additional logd?2 n factor in the preprocessing time, storage, and query-search time. For d 3, Subramanian and Ramaswamy [270] have proposed a data structure that can answer a range-reporting query in time O(logd?2 n log n + k) using O(n logd?1 n) space, and Bozanis et al.... In PAGE 18: ... Rectangle-rectangle searching is central to many applications because, in practice, polygonal objects are approximated by rectangles. Chazelle [58] has shown that the bounds mentioned in Table1 also hold for this problem. In practice, two general approaches are used to answer a query.... ..."

Cited by 205

### Table 1: Applicability of the Tangent-Secant Method rectangle size

"... In PAGE 2: ... For various sidelengths we determined how many squares of that sidelength per- mit an application of the tangent-secant method. The per- centages listed in Table1 indicate that the tangent-secant method becomes applicable early in the re nement process. Table 2: Accuracy of Real Root and Success of Tangent- Secant Stepfactor deg 10 deg 20 deg 30 1 50% 61% 71% 2?1 74% 80% 83% 2?2 82% 90% 90% 2?3 93% 94% 96% 2?4 96% 97% 97% 2?10 76 = 100% 173 =100% 268 = 100% An e cient implementation of the tangent-secant method must not use exact arithmetic.... ..."

### Table 1;; the preprocessing time of each data structure is O(n log n). If the query rectangles

"... In PAGE 10: ...tree of size O(n) to answer a planar range-reporting query in time O(log n + k)[208]. Problem Model Size Query time RAM n log n Counting APM n log n EPM n log 2 n n log n + k log quot; (2n=k) RAM n log log n log n + k log log(4n=k) n log quot; n log n + k Reporting APM n k log(2n=k) EPM n k log 2 (2n=k) n log n log log n log n + k Semigroup m log n log(2m=n) n log 2+ quot; n Semigroup RAM n log log n log 2 n log log n n log quot; n log 2 n APM n log 3 n EPM n log 4 n Table1 . Asymptotic upper bounds for planar orthogonal range searching, due to Chazelle [55, 58], in the random access machine (RAM), arithmetic pointer machine (APM), elementary pointer machine (EPM), and semigroup arithmetic models.... In PAGE 10: ... Asymptotic upper bounds for planar orthogonal range searching, due to Chazelle [55, 58], in the random access machine (RAM), arithmetic pointer machine (APM), elementary pointer machine (EPM), and semigroup arithmetic models. Each of the two-dimensional results in Table1 can be extended to queries in R d at a cost of an additional log d;2 n factor in the preprocessing time, storage, and query-search time. For d 3, Subramanian and Ramaswamy [270] have proposed a data structure that can answer a range-reporting query in time O(log d;2 n log n + k) using O(n log d;1 n) space, and Bozanis et al.... In PAGE 18: ... Rectangle-rectangle searching is central to many applications because, in practice, polygonal objects are approximated by rectangles. Chazelle [58] has shown that the bounds mentioned in Table1 also hold for this problem. In practice, two general approaches are used to answer a query.... ..."

### Table 1. Test Suites for Rectangle Source and Varying Orientations

1993

"... In PAGE 9: ... Consequently only uniform linear results are reported. Table1 . Test Suites for Rectangle Source and Varying Orientations Test 1 Linear Test 1 Struct Test 2 Linear Test 2 Struct Test 3 Linear Test 3 Struct Test 4 Linear Test 4 Struct Test 5 Linear Test 5 Struct 9.... In PAGE 10: ... In Test 4 the receiver plane slowly rotates towards the source and finally in Test 5 a rotated plane moves under the source. In Table1 , we see the results for a total of 75 tests. The first and last few cases in each suite are typically situa- tions where the tail regions are dominant.... ..."

Cited by 13

### Table 1 : EU policy towards regional competition

"... In PAGE 10: ... EU POLICY TOWARDS REGIONAL COMPETITION A broad range of EU policies explicitly or implicitly aim to avoid a race-to-the-bottom. As seen in Table1 , regional policy, fiscal harmonisation and social policy can be viewed from this perspective. For each of those policy fields, the table distinguishes between three regulatory strategies.... ..."

### Table 2. Data manipulation operations.*

"... In PAGE 4: ... The total data-base size is also an im- portant limitation for most of the systems; only ODYS- SEY, AGS, IBIS, and KANDIDATS are reported capable of handling data bases equivalent to more than 1000 polygons. Data manipulation and retrieval capabilities Other than input, editing, and output, Table2 shows all of the specific data manipulation operations that we were able to identify for the major systems. Few of the available references list their fundamental data manipu- COMPUTER... In PAGE 5: ... How- ever, we do not examine data input and editing capabil- ities in this article. Each system seems to perform only a small percentage of the total number of functions shown in Table2 . The grid systems do appear to perform a larger number of op- erations per system, on the average.... In PAGE 6: ...followed by tests for and calculations of intersections. The operations in Table2 rarely allow the user a choice of procedures to be followed; the parameters usually in- clude a map or image to be processed, numeric variables to be used in predefined arithmetic expressions, and sometimes the name of a point, line, or region. NIMS, POLYVRT, and SYMAP each have a small number of functions with user-specified options.... In PAGE 7: ... Each of these commands allows the definition of temporary variables, calculations using arbitrary num- bers of image variables within a window which moves over the entire image area, and restriction of retrieval and calculation to a set of logically defined regions. This new systpm can perform any of the opera,tions in Table2 using one or two commands. E Acknowledgment This work was supported by US National Science Foun- dation Grant MCS 78-16754.... In PAGE 7: ... Existing systems differ widely with respect to data ma- nipulation operations that they support. Table2 summar- izes the situation. Most of the operations shown in the table should be provided in a generalized image data man- agement system.... ..."