Mongodb aggregation pipeline algorithm performance - mongodb

Is there any documentation that talks about MongoDb aggregation pipeline operators' algorithm performance. For example: If I do a $merge involving 5 records and the same done on 500 records, what is the order of the algorithm? O(1) or O(n). Similarly, I would like know know what each operator is depdendent on. Please help

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How is the aggregation achieved with MongoDB

How is the aggregation achieved with MongoDB ?
using mongoDB for some near real time aggregation and how it scale if the aggregation pipeline results are large ?
Is there any performance tuning methods during aggregation
Is there any performance tuning methods during aggregation
There are many. You should refer the documentation about query optimization
using mongoDB for some near real time aggregation and how it scale if the aggregation pipeline results are large ?
Refer this
Limit the number of documents - to handle network demand
use projection to return only the necessary fields.

In mongodb Which is better to use- MapReduce or Aggregation pipeline?

Some blogs says that mapreduce is slower than aggregation. So which one is ideal to use?
If you go through the official document you can clearly see it written:
For most aggregation operations, the Aggregation Pipeline provides better performance and more coherent interface. However, map-reduce operations provide some flexibility that is not presently available in the aggregation pipeline.

Why aggregate+sort is faster than find+sort in mongo?

I'm using mongoose in my project. When the number of documents in my collection becomes bigger, the method of find+sort becomes slower. So I use aggregate+$sort instead. I just wonder why?
Without seeing your data and your query it is difficult to answer why aggregate+sort is faster than find+sort.
But below are the things that holds good on find and aggregate
A well indexed(Indexing that suits your query) data will always yield faster results on your find query.
The components of aggregation pipeline which you use on your aggregate query, more operations is directly proportional to more execution time.
When you go for aggregation pipeline you can create new fields such as sum, avg and so on, which is not possible in a find.
see this thread for more info
MongoDB {aggregation $match} vs {find} speed

When to use map reduce over Aggregation Pipeline in MongoDB?

While looking at documentation for map-reduce, I found that:
NOTE:
For most aggregation operations, the Aggregation Pipeline provides
better performance and more coherent interface. However, map-reduce
operations provide some flexibility that is not presently available in
the aggregation pipeline.
I did not understand much from it.
What are the use cases for using map-reduce over aggregation pipeline?
What flexibility does map-reduce provide?
How much delta is there in performance?
For one thing, Map/Reduce in MongoDB wasn't made for ad-hoc queries, there's considerable overhead to M/R. Even a very simple M/R operation on a small dataset can take in the hundreds of milliseconds because of that overhead.
I can't say much about the performance of M/R compared to the aggregation framework on large datasets in practice, but in theory, M/R operations on a large sharded database should be faster since the shards can run the operations largely in parallel.
As to the flexibility, since M/R actually runs javascript methods you have the full power of the language at your disposal. For example, let's say you wanted to group some data by the cosine of a field's value. Since there's neither a $cos operator in the aggregation framework, nor a meaningful way to build discrete buckets from continuous numbers (something like $truncate), the aggregation framework wouldn't help in that case.
So, in a nutshell, I'd say the use cases are
keeping the results of M/R in a separate collection and updating it from time to time (using the out parameter and merging the results)
Complex queries on large sharded data sets
Queries that are so complex that you can't use the aggregation framework. I'd say that's a pretty certain sign of a design flaw in the data structure, but in principle, it can help

Aggregation framework on full table scan

I know that aggregation framework is suitable if there is an initial $match pipeline to limit the collection to be aggregated. However, there may be times that the filtered collection may still be large, say around 2 million and the aggregation will involve $group. Is the aggregation framework fit to work on such a collection given a requirement to output results in at most 5 seconds. Currently I work on a single node. By performing the aggregation on a shard set, will there be a significant improvement in the performance.
As far as I know the only limitations are that the result of the aggregation can't surpass the limit of 16MB, since what it returns is a document and that's the limit size for a document in MongoDB. Also you can't use more than 10% of the total memory of the machine, for that usually $match phases are used to reduce the set you work with, or a $project phase to reduce the data per document.
Be aware that in a sharded environment after $group or $sort phases the aggregation is brought back to the MongoS before sending it to the next phase of the pipeline. Potentially the MongoS could be running in the same machine as your application and could hurt your application performance if not handled correctly.