We denote by NC(n) the set of non-crossing partition of {1,..., n}, and if this situation does not happen, then we call π a crossing partition.
Examples of non-crossing and crossing partitions are give in Figures 2 and 3. Figure 2 Non-crossing partition {{1, 3, 5}, {2}, {4}} of the set {1, 2, 3, 4, 5}. Figure 3 Crossing partition {{1, 3, 5}, {2, 4}} of the set {1, 2, 3, 4, 5}.
It is observed that across many scenarios, the cache privatization's average memory access time improved as the L1 cache miss rate increased and/or the cross-partition interconnect latencies increased.
Vertebraria: The roots of glossopterids have regular cross-partitions that give them the appearance of a vertebrate backbone.
Vertex-cut method The vertex-cut method is another type of partitioning technique that attempts to reduce the number of cross-partition vertexes.
Our proposed method merges partition pairs for increasing a graph partitioning measure, namely modularity [7], so as to reduce the total number of cross-partition edges.
METIS, proposed by Karypis and Kumar in 1998 [18], is one of the representative partitioning algorithms that focuses on reducing the number of cross-partition edges via the edge-cut method.
The commutation cost increases to the number of cross-partition vertexes/edges, because communication between different computers is required when parameters are updated by referring to adjacent vertexes/edges in remote computers.
Edge-cut method The edge-cut method is a graph partitioning approach that divides a graph into sets of sub-graphs by cutting edges so as to reduce the number of cross-partition edges.
The calculation is based on combinatorial computation using crossing partitions since the matrices are not free.
