enthought / enthought/distarray

Sorting spitballing

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enhancement
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Python
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Description

Some sorting ideas for consideration:
- It is fairly reliable that communication overhead and latency are the dominant factors, so we want to minimize the total amount of communication.
- In general, sorting requires an all-to-all communication step: every worker has to send and receive data to and from every other worker, so there is potentially a lot of communication.
- We want to minimize the all-to-all communication as much as possible.
- We also assume that sorting the local array is efficient and a solved problem.
- If we can get all the right data to each worker, then sort the data locally with a local sort, then we're done. So the problem reduces to getting the right data to each worker.
- If we allow the sorted array to have an irregular block distribution that does not match the distribution of the original array, then that gives a lot of flexibility.

Assume we have `n` workers that share a block-distributed distarray. Assume we have some way to choose `n-1` pivots that partition the global array into `n` sections such that the number of elements in section `i` equals the number of elements on worker with rank `i`. Then the sort can proceed as follows:
- Partition each worker's localarray into `n` sections using the `n-1

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