### Table R-TreeIndex

2004

### Table 2: Performance Losses in R-trees

2000

"... In PAGE 10: ... 5 Standard Index Alternatives We used the STR algorithm [17] to sort the data for bulk-loading into an R-tree [10], which is the canonical multidimensional AM, used in a variety of research and commercial systems. As shown in Table2 , we found that sorting and bulk-loading the data minimized the utilization and clustering loss over our query workload, leaving the largest performance losses for the R-tree 7 in excess coverage. Essentially, the only problem with a bulk-loaded R-tree is its sloppy BPs.... ..."

Cited by 11

### Table 2: Performance Losses in R-trees

2000

"... In PAGE 9: ... 5 Standard Index Alternatives We used the STR algorithm #5B18#5D to sort the data for bulk-loading into an R-tree #5B10#5D, which is the canonical multidimensional AM, used in a variety of research and commercial systems. As shown in Table2 , we found that sorting and bulk-loading the data minimized the utilization and clustering loss over our query workload, leaving the largest performance losses for the R-tree 7 in excess coverage. Essentially, the only problem with a bulk-loaded R-tree is its sloppy BPs.... ..."

Cited by 11

### Table 2. Results summary of R-tree query performance experiments

2006

"... In PAGE 10: ...ig. 4. Leaf-nodes in the R-tree representing World Populated Places. Because the path through the index is replicated as well as the results of the query, subsequent queries can make use of relevant portions of the index. Table2 shows how some simple queries are affected by this caching property. For each test condition, we measured the time cost of performing a query on an empty local venue, thus inducing index replication over the network.... ..."

Cited by 1

### Table 2: No. of R-tree Node Accesses for CZ-Distance Joins

"... In PAGE 19: ... For small CZ values, on the other hand, C0CB-KDJ algorithm was slightly better than the other algorithms, due to its more localized node access patterns for small CZ. Table2 compares the number of R-tree nodes that would be fetched from disk with R-tree buffer size set to zero. Apparently, the bi-directional node expansion used by BU-KDJ and BTC5-KDJ algorithms requires much less number of R-tree node accesses than uni- directional node expansion used by C0CB-KDJ algorithm.... In PAGE 19: ... Apparently, the bi-directional node expansion used by BU-KDJ and BTC5-KDJ algorithms requires much less number of R-tree node accesses than uni- directional node expansion used by C0CB-KDJ algorithm. It should be noted that the number of R-tree node accesses for BU-KDJ, BTC5-KDJ and CBC2-SORT algorithms are all identical in Table2 . This is because these algorithms use the same bi-directional node expansion and access the same collection of R-tree nodes, though they may traverse an R-tree index in different orders.... ..."

### Table 2: No. of R-tree Node Accesses for CZ-Distance Joins

"... In PAGE 19: ... For small CZ values, on the other hand, C0CB-KDJ algorithm was slightly better than the other algorithms, due to its more localized node access patterns for small CZ. Table2 compares the number of R-tree nodes that would be fetched from disk with R-tree buffer size set to zero. Apparently, the bi-directional node expansion used by BU-KDJ and BTC5-KDJ algorithms requires much less number of R-tree node accesses than uni- directional node expansion used by C0CB-KDJ algorithm.... In PAGE 19: ... Apparently, the bi-directional node expansion used by BU-KDJ and BTC5-KDJ algorithms requires much less number of R-tree node accesses than uni- directional node expansion used by C0CB-KDJ algorithm. It should be noted that the number of R-tree node accesses for BU-KDJ, BTC5-KDJ and CBC2-SORT algorithms are all identical in Table2 . This is because these algorithms use the same bi-directional node expansion and access the same collection of R-tree nodes, though they may traverse an R-tree index in different orders.... ..."

### Table 1. R-trees versus O-trees for intersection queries on line (a) and polygon (b) data

2000

"... In PAGE 6: ... In our experiments it improves index accesses by AP BEB1, and reduces the number of results by AP BFB1 for lines and AP BDBEB1 for polygons for both R-trees and O-trees. Table1 (a) shows the comparison for line data, giving the the number of index accesses, results and leaf nodes which include an answer, the sum of index and results accesses as... In PAGE 7: ... The extra index accesses from the height outweigh the small gains in terms of less answers. Table1 (b) shows the comparison for polygon data. Here we see that the O-trees require more index accesses even when the height of the O-tree is equal to the R-tree.... ..."

Cited by 2

### Table 1 presents the average execution time for 50 win- dow queries on each data set, starting with a cold buffer pool. The same queries are executed for all data sets. The query windows are random polygons with 100 vertices each, and their MBRs are squares with an area of 1% of the area of the space. The centers of these MBRs are randomly chosen from the centers of the data polygon MBRs. R-tree indexes are available for all data sets, and they are used by all the queries.

2000

"... In PAGE 8: ... Table1 . Cost of a query with MBR area = 1% of space There is a significant difference in execution time be- tween the three data sets.... In PAGE 8: ... Even if such a cost model accurately estimates the execution time for one data set, it will be inaccurate for the other two. Table1 also illustrates the significance of the cost of re- finement, thereby validating one of the main premises of this paper. If we take the execution time for the 10-vertex data set to be an approximation of the filtering time for all three data sets, we see that refinement for the 1000-vertex data set is over an order of magnitude more expensive than filtering.... ..."

Cited by 21

### Table 1 presents the average execution time for 50 win- dow queries on each data set, starting with a cold buffer pool. The same queries are executed for all data sets. The query windows are random polygons with 100 vertices each, and their MBRs are squares with an area of 1% of the area of the space. The centers of these MBRs are randomly chosen from the centers of the data polygon MBRs. R-tree indexes are available for all data sets, and they are used by all the queries.

"... In PAGE 8: ... Table1 . Cost of a query with MBR area =1%of space There is a significant difference in execution time be- tween the three data sets.... In PAGE 8: ... Even if such a cost model accurately estimates the execution time for one data set, it will be inaccurate for the other two. Table1 also illustrates the significance of the cost of re- finement, thereby validating one of the main premises of this paper. If we take the execution time for the 10-vertex data set to be an approximation of the filtering time for all three data sets, we see that refinement for the 1000-vertex data set is over an order of magnitude more expensive than filtering.... ..."