alamb opened a new issue, #7065:
URL: https://github.com/apache/arrow-datafusion/issues/7065

   ### Is your feature request related to a problem or challenge?
   
   Making aggregations fast in datafusion helps its adoption and makes it even 
cooler
   
   As part of the new #6904  work, @yjshen  had an idea 
https://github.com/apache/arrow-datafusion/pull/6800#discussion_r1251142165 
that could avoid a copy in the accumulator implementations:
   
   
   
   ### Describe the solution you'd like
   
   ```Adaptive sizing(perhaps?): How would the hash table header and states in 
each accumulator initialize and grow their sizes afterward?```
   
   Here is the structure of the current group operator
   
   ```
                                            ┌──────────────┐   ┌──────────────┐ 
  ┌──────────────┐
                                            │┌────────────┐│   │┌────────────┐│ 
  │┌────────────┐│
       ┌─────┐                              ││accumulator ││   ││accumulator ││ 
  ││accumulator ││
       │  5  │                              ││     0      ││   ││     0      ││ 
  ││     0      ││
       ├─────┤                              ││ ┌────────┐ ││   ││ ┌────────┐ ││ 
  ││ ┌────────┐ ││
       │  9  │                              ││ │ state  │ ││   ││ │ state  │ ││ 
  ││ │ state  │ ││
       ├─────┤                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       │     │                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       ├─────┤                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       │  1  │                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       ├─────┤                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       │     │                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       └─────┘                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
                                            ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
                                            ││ └────────┘ ││   ││ └────────┘ ││ 
  ││ └────────┘ ││
                                            │└────────────┘│   │└────────────┘│ 
  │└────────────┘│
       Hash Table                           └──────────────┘   └──────────────┘ 
  └──────────────┘
                                                                                
                  
                                             New NewAccumulator                 
                  
                                                                                
                  
                                                                                
                  
                                                                                
                  
   stores "group indexes"                     There is one GroupsAccumulator 
per aggregate           
   which are indexes into                     (NOT PER GROUP). Internally, each 
                  
   Vec<GroupState>                            GroupsAccumulator manages the 
state for                
                                              multiple groups                   
                  
   ```
   
   The implementation of this, such as Average (TODO link) is to use a 
`Vec<T>`. While this approach is simple to implement, it also means that as the 
Vec grows, the accumulated vales may be copied (up to 2 times on average, given 
a doubling strategy)
   
   An alternate, suggested by @yjshen  is to segment the state into 
**fixed-sized vectors, allocate a new vector at a time**, fill it until full, 
then create a new vector for upcoming new states.
   
   ```
                                            ┌──────────────┐   ┌──────────────┐ 
  ┌──────────────┐
                                            │┌────────────┐│   │┌────────────┐│ 
  │┌────────────┐│
       ┌─────┐                              ││accumulator ││   ││accumulator ││ 
  ││accumulator ││
       │  5  │                              ││     AGG    ││   ││     SUM    ││ 
  ││     0      ││
       ├─────┤                              ││ ┌────────┐ ││   ││ ┌────────┐ ││ 
  ││ ┌────────┐ ││
       │  9  │                              ││ │ state- │ ││   ││ │ state- │ ││ 
  ││ │ state  │ ││
       ├─────┤                              ││ │segment-│ ││   ││ │segment-│ ││ 
  ││ │        │ ││
       │     │                              ││ │   1    │ ││   ││ │   1    │ ││ 
  ││ │        │ ││
       ├─────┤                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       │  1  │                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       ├─────┤                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       │     │                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
       └─────┘                              ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
                                            ││ │        │ ││   ││ │        │ ││ 
  ││ │        │ ││
                                            ││ └────────┘ ││   ││ └────────┘ ││ 
  ││ └────────┘ ││
                                            ││            ││   ││            ││ 
  │└────────────┘│
       Hash Table                           ││ ┌────────┐ ││   ││ ┌────────┐ ││ 
  └──────────────┘
                                            ││ │ state- │ ││   ││ │ state- │ ││ 
                  
                                            ││ │segment-│ ││   ││ │segment-│ ││ 
                  
                                            ││ │   2    │ ││   ││ │   2    │ ││ 
                  
                                            ││ │        │ ││   ││ │        │ ││ 
                  
                                            ││ │        │ ││   ││ │        │ ││ 
                  
                                            ││ │        │ ││   ││ │        │ ││ 
                  
                                            ││ │        │ ││   ││ │        │ ││ 
                  
                                            ││ │        │ ││   ││ │        │ ││ 
                  
                                            ││ │        │ ││   ││ │        │ ││ 
                  
                                            ││ └────────┘ ││   ││ └────────┘ ││ 
                  
                                            │└────────────┘│   │└────────────┘│ 
                  
                                            └──────────────┘   └──────────────┘ 
                  
                                                                                
                  
   ```   
   
   Thru this segmented approach, we could avoid memory copy for each resize, 
which the number of resizing would be great for high cardinality aggs, and 
grows the size more predictably. 
   
   But admittedly, this approach would also bring complexity for both header 
pointer management and update span multiple vectors.
   
   
   
   ### Describe alternatives you've considered
   
   _No response_
   
   ### Additional context
   
   _No response_


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