
Type: New Feature

Status: In Progress

Priority: Minor

Resolution: Unresolved

Affects Version/s: 3.0.0

Fix Version/s: None

Component/s: GraphX

Labels:None
Recently, I found a new partition strategy (call EdgePartitionTriangle), which is a combination of the partition strategy EdgePartition2D and the the partition strategy CanonicalRandomVertexCut. This partition strategy has three advantages：
1. nicer bound on vertex replication, sqrt(2 * numParts).
2. colocate all edges between two vertices regardless of direction.
3. same work balance compared with EdgePartition2D
See https://github.com/weiwee/edgePartitionTri/blob/master/EdgePartitionTriangle.ipynb
The main idea is to virtually partitioned by EdgePartition2D, gets partitions
{(i,j)i=1,2,..,k, j=1,2,..,k}. Then relocate partitions by folding the virtual partitions, such as:
(1,0) and (0,1) > (1, 0)
(2,1) and (1,2) > (2, 1)
...
(k, k1) and (k1, k) > (k, k 1)
Finally, maps {(1,0), (2,0), (2,1), (3,0),(3,1),(3,2),...,(k, k1)} to {0,1,...,k*(k1) / 2}
The complete method needs to handle more details：
1. when numParts is not a triangle number, partitions are divided into two types: triangleParts and rests. The later one is partitioned by a different strategy.
2. when edges are virtually located to partition (a, a), Then they should be relocated to partition
{(a, 0), (a, 1),..., (a, a1), (a+1, a),...,(k, a)}to achieve better work balance.
codes:
object EdgePartitionTriangle extends PartitionStrategy { override def getPartition(src: VertexId, dst: VertexId, numParts: PartitionID): PartitionID = { val mixingPrime: VertexId = 1125899906842597L val numRowTriParts = ((math.sqrt(1 + 8 * numParts)  1) / 2).toInt val numTriParts = numRowTriParts * (numRowTriParts + 1) / 2 val segmentFactor = 100 // positive even numbers val numSegments = (segmentFactor * math.sqrt(4 * numParts * numTriParts)).toInt val segRow = (math.abs(src * mixingPrime) % numSegments).toInt val segCol = (math.abs(dst * mixingPrime) % numSegments).toInt var row = segRow / (segmentFactor * numRowTriParts) var col = segCol / (segmentFactor * numRowTriParts) if (math.max(segRow, segCol) >= 2 * segmentFactor * numTriParts) { row = numRowTriParts + 1 col = math.min(segRow, segCol) % (numParts  numTriParts) } else if (row == col) { val ind = math.min(segRow % numRowTriParts, segCol % numRowTriParts) col = (math.min(2 * numRowTriParts  ind  1, ind) + row + 1) % (numRowTriParts + 1) } if (row > col) row * (row  1) / 2 + col else col * (col  1) / 2 + row }