ABCDEFGHIJKLMNOPQRSTUVWXYZ
1
1.sort get identity slices;
2.transform on keys;
3.merge partitions by keys		1.transform on all hidden part columns and build extra cols (if there are hidden part columns)
2.existing sort algorithm to group and find keys		1.transform on all part columns;
2.one-scan bucket sort
2
hidden partition on all part columnspartitions ++compared to 2E:
- := bucket sort faster than raw sort
 + := easy algorithm
compare to 2E:
- := sort not efficient
compare to 2C:
- := slightly more extra transform (almost same)
compared to 2C see 2C
3
hidden partition on all part columnspartitions --compared to 3E:
- := bucket sort faster than raw sort
+ := aspy and transform less		 + := easy algorithm
compare to 3E:
- := sort not efficient
compare to 3C:
- := much more extra transform
compared to 3C see 3C
4
hidden partition on subset of part columnspartitions ++compared to 4E:
- := bucket sort faster than raw sort
x := number of idenity cols		 + := easy algorithm

compare to 3C:
- := slightly more extra transforms
x := number of idenity cols
5
hidden partition on subset of part columnspartitions --compared to 4E:
- := bucket sort faster than raw sort
+ := aspy and transform less
x := number of idenity cols		 + := easy algorithm

compare to 3C:
- := much more extra transforms
x := number of idenity cols
6
no hidden parts, all identity part columnspartitions ++N/A because no need to do step 2 and 3, so 6C and 6D are the sameexisting algorithmcompared to 6D
-:= much more transform than no transform
+:= bucket sort is fast
7
no hidden parts, all identity part columnspartitions --N/A because no need to do step 2 and 3, so 7C and 7D are the sameexisting algorithmcompared to 7D
-:= more transform than no transform
+:= bucket sort is fast
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100