Decomposition.md

@@ -4,10 +4,24 @@ Every structure should divide the information that they store across processors,
 * Data driven decomposition
 * Fixed decomposition
 
-The fist approach try to generate a model for the interaction across processors and try to minimize the space
+The fist approach try to create a model for the interactions across processors and try to minimize the space
 
 The second instead try to divide the quantity of information the structure store without considering the interactions
 
 ## Model decomposition
  
-The modular structure of OpenFPM give the possibility to create distributed structure with different decomposition strategies.
+In a distributed-memory setting, where data are scattered across
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+processors, two factors are important: equal division of work across
+processors and reduction of the communication overhead.
+A typical approach, is to formulate the problem as a 
+graph-partitioning problem: the physical domain is divided into sub-domains
+ (vertices of the graph), each of them  carrying a weight modeling the computational cost.
+ The communication pattern between sub-domains is represented as links
+between the sub-domains (edges of the graph) with weights formalizing
+the communication cost. The requirement of balanced computation with
+minimal communication then translates to the optimization problem of
+finding a graph partitioning where each group contains the same sum of
+weights, and the sum of the cut edges is minimal. Even if a model decomposition
+it is not bind to a graph model it is true that until now is the main approach
+
+* CartDecomposition
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