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https://issues.apache.org/jira/browse/FLINK-23893?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17402096#comment-17402096
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Yangze Guo commented on FLINK-23893:
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A slot request contains multiple dimensions resources. So, it is indeed a 
multi-dimensional packing problem, which is NP-hard. I agree that we should 
document it and maybe find another suboptimal strategy in the future.

> Fine-grained resource allocation may fail depending on slot allocation order
> ----------------------------------------------------------------------------
>
>                 Key: FLINK-23893
>                 URL: https://issues.apache.org/jira/browse/FLINK-23893
>             Project: Flink
>          Issue Type: Bug
>          Components: Runtime / Coordination
>            Reporter: Chesnay Schepler
>            Priority: Minor
>             Fix For: 1.14.0
>
>
> The fine-grained slot management is relatively simple in that it iterates 
> over each registered TM in order for each required slot.
> This means that you can pretty easily create scenarios where, depending on 
> the slot order, the allocation of a slot may fail.
> A trivial example, only using memory for conciseness:
> 2 TMs with 3 MB of memory each
> 2 slot-sharing groups with parallelism=2 and the following requirements:
>  1) 1 MB memory
>  2) 2 MB memory
> If both sub-tasks of 1) are scheduled first on a single TM then the job 
> cannot be scheduled.
> It's not terrible for this limitation to exist in the first version, but it 
> should be _explicitly_ documented.



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