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Say I have a hadoop cluster where one node is the Master node and the other is a Data node. The slave node is an 8-core machine just to make sure there are enough cores to process jobs parallelly. Can i still split the file into say 3 blocks and have the slave node store all the three blocks separately on it. In other words, "if we want to utilize all the slave nodes in a hadoop cluster", then is there a 1:1 relation between number of slave nodes and the maximum number of blocks of a file? If yes, then in such a case how would the map-reduce work. Will the master node fire three map jobs to the slave node and have each mapper pick up each block on the slave node? My question can be seen in a different way. If we have a 1GB file on a cluster with 3 data nodes then how do the 64 MB blocks get divided and how are they distributed between the three nodes?

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The second question seems to be more understandable for me so I will take that first.

From HDFS Perspective:

With 64MB block size a 1GB file consists from 16 blocks, blocks are being stored somewhat randomly between DataNodes, if you have more from them as the replication factor, but you can expect an even distribution between the nodes, if you do not load the data from one of the DNs. If you do, that DN will hold a replica from all the blocks, and other DNs will hold the remaining replicas distributed sort of evenly (still randomly placed). So yes, if you have a file consists from 16 blocks, and only 3 DN with a replication factor of 3 all 3 DNs will hold all 16 blocks for example.

From YARN's perspective when you run the MapReduce job:

YARN tries to find a container on a node for a mapper that has the data locally, there is a configurable wait time for a free container on such nodes before YARN starts up the mapper on a node that does not have the data.

YARN does not rely on physical cores directly, you can configure the number of virtual cores and the amount of memory a container uses, and based on these values YARN will allocate the amount of available containers in a NodeManager.

Further reading on YARN tuning on Cloudera Engineering blog

However:

From the first part of the question as I understand you want to achieve paralellism by defining the block size to split your data files.

MapReduce does not care about HDFS blocks, it has its own abstraction to split the input, it is called InputSplit. InputSplits are feeded to the mappers, by the InputFormat. Also InputSplits are defining the place where the split is available locally so that YARN can find a container that is on a node that has the split on local data storage. I suggest to check the API, and the available implementations of InputFormat, as they most likely suit your needs, however if they are not, then you can still write your own implementation, and specify it via the job configuration.