[Minor] Fix comments for GraphX 2D partitioning strategy
The sum of vertices on matrix (v0 to v11) is 12. And, I think one same block overlaps in this strategy. This is minor PR, so I didn't file in JIRA. Author: kj-ki <kikushima.kenji@lab.ntt.co.jp> Closes #3904 from kj-ki/fix-partitionstrategy-comments and squashes the following commits: 79829d9 [kj-ki] Fix comments for 2D partitioning.
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@ -32,9 +32,9 @@ trait PartitionStrategy extends Serializable {
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object PartitionStrategy {
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/**
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* Assigns edges to partitions using a 2D partitioning of the sparse edge adjacency matrix,
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* guaranteeing a `2 * sqrt(numParts)` bound on vertex replication.
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* guaranteeing a `2 * sqrt(numParts) - 1` bound on vertex replication.
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*
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* Suppose we have a graph with 11 vertices that we want to partition
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* Suppose we have a graph with 12 vertices that we want to partition
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* over 9 machines. We can use the following sparse matrix representation:
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*
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* <pre>
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@ -61,7 +61,7 @@ object PartitionStrategy {
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* that edges adjacent to `v11` can only be in the first column of blocks `(P0, P3,
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* P6)` or the last
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* row of blocks `(P6, P7, P8)`. As a consequence we can guarantee that `v11` will need to be
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* replicated to at most `2 * sqrt(numParts)` machines.
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* replicated to at most `2 * sqrt(numParts) - 1` machines.
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*
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* Notice that `P0` has many edges and as a consequence this partitioning would lead to poor work
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* balance. To improve balance we first multiply each vertex id by a large prime to shuffle the
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