### Table 1: Iteration space partitions for candidate atomset generation (Query1)

2004

"... In PAGE 6: ....2.1 Candidate atomset generation In Section 3, we discussed a simple approach to parti- tion the iteration space for candidate atomset generation. Table1 and Table 2 present the number of candidate atom- sets generated at each level by each processor, when using 4 processors, for Query 1 and Query 2 respectively. The pa- rameters for Query 1 and Query 2 are (support=70, fuzzi- ness=2, resolution=0.... ..."

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### Table 2: Iteration space partitions for candidate atomset generation (Query2)

2004

"... In PAGE 6: ....2.1 Candidate atomset generation In Section 3, we discussed a simple approach to parti- tion the iteration space for candidate atomset generation. Table 1 and Table2 present the number of candidate atom- sets generated at each level by each processor, when using 4 processors, for Query 1 and Query 2 respectively. The pa- rameters for Query 1 and Query 2 are (support=70, fuzzi- ness=2, resolution=0.... ..."

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### Table 3n3a Regular space partitioning n7c simulation results

"... In PAGE 28: ... The reason is that in our implementation the criterion of putting an object onto the list assigned to a given spatial cell is not perfectly that the object intersects the cell but weaker than thatn3a an object is put onto the list if there is no face of the cell the plane of which separates the object from the cell. There is one more interesting observation in the case of regular space partitioning n28 Table3 n29. There is a small but persistent n0ductuation in the average number of intersection tests n28 N I n29n2c with local minima at n n3d 50000 and n n3d 500000n2c which is independentofc.... ..."

### Table 2: Topological and directional relations. Topological relations characterize the fact that spatial areas may overlap, touch or be disjoint. Directional relations concern the order of spatial objects. They are used as a selection criterion dividing the space in partitions, e.g., Grenoble is contained in the 3A and B are respectively component[1] and component[2]. 10

"... In PAGE 11: ... Spatial aspects have been widely studied by geographical information and spatial database systems [EF91, GG98, PKA99]. Table2 presents topological and... ..."

### Table 3: Regular space partitioning | simulation results 29

### Table 2.1 summarizes the main features of out-of-core simplification techniques. For each method, we list: the type of input (Dataset); the type of space partition adopted (Partitioning); the type of approach (Simplification); the possibility to build a multi-resolution model based on the specific simplification technique (Multi-res); and the space requirements in main memory (Space). The algorithms by Hoppe [20], Prince [37] and Magillo and Bertocci [33] are designed for either regular or irreg- ular terrain data, while all the other technique can handle arbitrary triangle meshes describing the boundary of 3D objects. When applied to terrain simplification, al- gorithms based on space partitioning should be modified by replacing the octree which partitions 3D space with a simpler quadtree partition of the 2D domain of the TIN. Note that only methods based on space partitioning are suitable to build multi-resolution models.

### Table 3(a). The 6-dimensional 8PSK modulation signal space partition I. Partition

1986

"... In PAGE 44: ... To read these tables, we only need to understand the corresponding binary vector space partition. We show this by going through the partition given in Table3 (a). From Table 3(a), we first find the binary linear block codes used in the binary vector space partitions: c1 : (3,2) code, G~ = [h :I, m-(cl) = 2; C2 : (3, 1) code, G2 = [O 1 11, HD~ amp;) = 2; C3 : (3, 0) code, C3 = (0 0 01, HDdn(C3) = -; and C4 = C1, C5 = Cp Let C = (0, lQ, the 3-dimensional binary vector space.... In PAGE 47: ... Four-state R = 8/9 trellis coded 6-dimensional 8PSK modulation This time we have two different signal space partitions. First consider partition 11 given in Table3 (b). Since R = 8/9, there are 28 = 256 transitions to and from each state.... In PAGE 48: ...33 bitddimension . If partition I of Table3 (a) is used instead, the best trellis structure will be the one with four sets of 64 parallel transitions. It also achieves dj = 34 = 1.... In PAGE 49: ...,, b2 , . . . , b9 is shown in Table 6, which is obtained from the signal space partition of Table3 (b). From Table 6 we see that bl, b2, b4, b5, b7, and b8 can be either 0 or 1 ... In PAGE 70: .... 1 r Table3 (b). The 6-dimensional 8PSK modulation signal space partition II.... ..."

### Table 3: Summary of algorithms extracting DFA through searching in a state space partitioned by vector quantisation.

2005

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