Rearranging data among processing elements of computational memory

A computing system comprising:

• one or more processors configured to collectively:
• model an array of interconnected processing elements as a graph of nodes, wherein each layer of the graph represents a possible arrangement of data elements within the array of interconnected processing elements, and wherein an edge between nodes of adjacent layers of the graph represents a movement of a data element between the nodes;
• set a first constraint as a starting arrangement of the data elements stored in the array of interconnected processing elements;
• set a second constraint as an ending arrangement of the data elements stored in the array of interconnected processing elements;
• set a third constraint to limit each node of the graph to have one input edge from a previous layer and one output edge to a subsequent layer;
• select a number of layers for the graph based on a ratio of a greatest distance among the interconnected processing elements of the array to a maximum possible movement distance among PEs;
• process the model, the first constraint, the second constraint, and the third constraint with an integer programming solver to obtain a program of movements of data elements among the interconnected processing elements, wherein the program implements a rearrangement of the data elements from the starting arrangement to the ending arrangement;
• if the integer programming solver determines that the program is unattainable in the selected number of layers, then increase the number of layers for the graph and reperform the process with the integer programming solver;
• and
• store the program for execution by a controller of the interconnected processing elements when the rearrangement is to be performed.

A method comprising

• modelling an array of interconnected processing elements as a graph of nodes, wherein each layer of the graph represents a possible arrangement of data elements within the array of interconnected processing elements, and wherein an edge between nodes of adjacent layers of the graph represents a movement of a data element between the nodes;
• setting a first constraint as a starting arrangement of the data elements stored in the array of interconnected processing elements;
• setting a second constraint as an ending arrangement of the data elements stored in the array of interconnected processing elements;
• setting a third constraint to limit each node of the graph to have one input edge from a previous layer and one output edge to a subsequent layer;
• selecting a number of layers for the graph based on a ratio of a greatest distance among the interconnected processing elements of the array to a maximum possible movement distance among PEs;
• processing the model, the first constraint, the second constraint, and the third constraint with an integer programming solver to obtain a program of movements of data elements among the interconnected processing elements, wherein the program implements a rearrangement of the data elements from the starting arrangement to the ending arrangement;
• if the integer programming solver determines that the program is unattainable in the selected number of layers, then increasing the number of layers for the graph and reperforming the processing with the integer programming solver;
• and
• storing the program for execution by a controller of the interconnected processing elements when the rearrangement is to be performed.