Enumerator for Optimal Plans in DMLProgram

[min-guk]

Summary

An initial version of the recursive function for finding the optimal plan in a DMLProgram has been implemented. This design is based on FederatedPlannerFedAll. This PR addresses a different topic from the previous one (#2175), despite being related, so it has been created separately.

The currently implemented functionalities are as follows:

• Recursive traversal (enumeration?) of StatementBlock and Statement within the program.
• Identification of the optimal federated plan (FedPlan) for each Statement (limited to individual statements, not the entire program).

However, the current implementation does not yet support:

• Integration and identification of the optimal FedPlan and MemoTable at the StatementBlock or program level.

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Questions for Discussion

1. Recursive Integration of Optimal FedPlans and MemoTables Across Statements and StatementBlocks

• Should the same dynamic programming approach be used for integration?
• Or would simply summing up the minimal plans of each block/statement suffice?

2. MemoTable Sharing

• Is there a need to share the MemoTable?
• Are there data/hop dependencies between statements?

3. Prediction of Iteration Counts for Loops (For and While)

How should the iteration counts for loops be determined?

• If from/to/increment are constants: Calculations can be done at compile time.
• If they are variables: Use default values at compile time, adjust at runtime, or predict using ML models.

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