### Table 7: Rent parameters for random and recursive partitioning of random graphs.

### Table 1n3a Index Vector by Recursion

in Bit reversal � hierarchical memory � Fast Fourier Transform c�Copyright Hewlett�Packard Company 1993

1993

"... In PAGE 4: ... For examplen2c we know that the last n n00 2 bits of n7e k j are zero for k j n3c 4. This approach leads to the recursive algorithm illustrated in Table1 n5b36n5d. At each step wemultiply the current list by 2 and concatenate 1 plus the list.... In PAGE 30: ...Table1 0n3a Bit Reversals on 3090 Vector in cycles per element Version 15 16 17 18 19 20 21 22 cvl143n5b33n5d 30.2 39.... In PAGE 31: ...Table1 1n3a Bit Reversals on RSn2f600n2d520 in cycles per element Version 12 13 14 15 16 17 18 19 20 21 cooleyn5b7n5d 15.9 16.... In PAGE 32: ...Table1 2n3a Bit Reversals on HPn2d730 in cycles per element Version 12 13 14 15 16 17 18 19 20 21 cooleyn5b7n5d 19.4 19.... In PAGE 33: ...Table1 3n3a Bit Reversals on Intel i860 in cycles per element Version 8 9 10 11 12 13 14 15 16 17 cooleyn5b7n5d 27.3 26.... ..."

### Table 3: The edge-cuts produced by the multilevel recursive bisection, multilevel recursive bisection, and multilevel k-way partition.

1998

Cited by 333

### Table 3: The edge-cuts produced by the multilevel recursive bisection, multilevel recursive bisection, and multilevel k-way partition.

1998

Cited by 333

### Table 5.2 Comparison of string and array implementations of spatial indexes

1994

### Table 4: Performance of the Recursive Partitioning Algorithm. The method is around 3 times faster than the L-Algorithm with raster points and around 60 times faster than the L-Algorithm (without raster points) as introduced in [16].

in An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

2007

"... In PAGE 19: ...oints. Using raster points, the method is around 20 times faster (Cover IIA and IIB). Note that the usage of the raster point in an efficient way was possible due to using the simple-but-effective indexation suggested in [6]. Table4 presents the performance of the Recursive Partitioning Algorithm. The reduc- tions of the runtimes, when compared with only applying the L-Algorithm, are very large.... In PAGE 19: ...42 seconds (Table 3) to 0.71 seconds ( Table4 ). The Recursive Partitioning Algorithm optimally solved all the problems in Cover IA, IIA, IB and IIB, as well as 97,046 (over a total of 98,016) of the instances in Cover IIIB - the solutions of the remaining 970 examples are not proven optimal.... ..."

### Table 4: Performance of the Recursive Partitioning Algorithm. The method is around 3 times faster than the L-Algorithm with raster points and around 60 times faster than the L-Algorithm (without raster points) as introduced in [16].

in An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

2007

"... In PAGE 19: ...oints. Using raster points, the method is around 20 times faster (Cover IIA and IIB). Note that the usage of the raster point in an efficient way was possible due to using the simple-but-effective indexation suggested in [6]. Table4 presents the performance of the Recursive Partitioning Algorithm. The reduc- tions of the runtimes, when compared with only applying the L-Algorithm, are very large.... In PAGE 19: ...42 seconds (Table 3) to 0.71 seconds ( Table4 ). The Recursive Partitioning Algorithm optimally solved all the problems in Cover IA, IIA, IB and IIB, as well as 97,046 (over a total of 98,016) of the instances in Cover IIIB - the solutions of the remaining 970 examples are not proven optimal.... ..."

### Table 1: Partition sizes and partition access probabilities for the partitioning sets used in this

"... In PAGE 11: ...ndex tree, i.e., when Index Bu er Size Total Index Size =1:0, all the pages in the index tree ts in memory. In this study,wehavechosen ve access patterns, the partition sizes and access probabil- ities are summarized in Table1 (note that this is the OID access pattern, and not the index page access pattern). We call each of these patterns a partitioning set.... ..."

### Table 6: Rent parameters for direct q-way partitioning and recursive bipartitioning.

### Table 2. The spatial joins of the experiments

"... In PAGE 3: ... The file is derived from the total set of street lines of California. In Table2 some of the spa- tial joins are described which we performed in our experiments. The selectivity refers to the number of results divided by the product of the number of MBRs of the input relations.... In PAGE 5: ... Temporary storing result tuples and duplicate removal in a separate phase is avoided at the additional cost of at most six comparisons (when a result is detected) which are required for computing the reference point and test- ing the point being in the region of the partition. In order to show the impact of the new method for duplicate removal we present the results of the exper- iments of spatial joins J1-J4 (see Table2 ). We assume here that the size of the available main memory is 2.... ..."