Hi Vladimir,

I'm a bit late, sorry. My comments below:

Feels like our Reducer is more of an Combiner as described by [1], as it enforce the result of the reduce (KOut) to have the same type as the entries it consumes (KOut).
Don't you think that if we add the Combiner/MapCombineCommand we can loosen up this constraint and allow the Reducer to output something else than KOut?

Once loaded into target execution node MapCombineCommand takes each 
local KIn key and executes Mapper method  void map(KIn key, VIn value, 
Collector<KOut, VOut> collector). Results are collected to a common 
Collector<KOut, VOut> collector and combine phase is initiated. A 
Combiner, if specified, takes KOut keys and imediatelly invokes reduce 
phase on keys. The result of mapping phase executed on each node is 
<KOut, VOut> map M. There will be one resulting M map per execution node N.

So the combiner has the same output as the Mapper - just that this time it is in the form of an Map<KOut, VOut> instead of a Collector<Kout,Vout>?
Which is okay IMO, as at the end of the day the Combiner is just an extra polishing added to the mapping...

At the end of combine phase instead of returning map M to the master 
task node (as we currently do), we now hash each KOut in map M and group 
KOut keys by the execution node N they are hashed to. Each group of KOut 
keys and its VOut values, hashed to the same node, is wrapped with a new 
command Migrate. Command Migrate, which is very similar to 
PutKeyValueCommand,executed on Infinispan target node N esentially 
maintains KOut K -> List<VOut> mapping, i.e all KOut/VOut pairs from all 
executed MapCombineCommands will be collocated on a node N where KOut is 
hashed to and value for KOut will be a list of all VOut values. We 
essentially collect all VOut values under each KOut for all executed 
MapCombineCommands.

This potentially involves each node sending some state to all other nodes, i.e. (clusterSize-1)^2 RPCs. Not that this is necessarily a bad thing, as it is there to reduce contention on a single node.

At this point MapCombineCommand has finished its execution; list of KOut 
keys is returned to a master node and its MapReduceTask. We do not 
return VOut values as we do not need them at master task node. 
MapReduceTask is ready to start with reduce phase.

If you plan to add this to a design document, I think it would be a good idea to show an example of how the combiner would be used with the word numbering algorithm. You explained this quite well here, but that would make sure we're all on the same page on the role of combiner :-) 

Reduce phase


MapReduceTask initializes ReduceCommand with a user specified Reducer. 
For each key KOut collected from a map phase we group them by execution 
node N they are hashed to. For each node N and its grouped input KOut 
keys MapReduceTask creates a ReduceCommand and sends it to a node N 
where KOut keys are hashed.

the originator (node on which the M/R is run), at this point, doesn't know the entire set of KOut values produces, so it can't determine the list of nodes where to send the ReduceCommand - it would have to send it to all nodes, right?