An Improved Algorithm for Array Alignment

Experimental Evaluation of Automatic Array Alignment in Parallelized Matlab

“…The obvious heuristic is to maximize the length of the spanning tree [17] or, similarly, minimize the length of fundamental circuits [30], as this guarantees the alignment for the most expensive operations. However, this does not always lead to a globally optimal alignment, and an improved heuristic called GPM (greedy potential minimization) [24] starts from a longest tree and explores adjacent spanning trees in the fashion of gradient descent optimization. The GPM algorithm was shown to be better than other state-of-the art solutions such as the compact dynamic programming (CDP) techniques [4] using Monte Carlo simulations on synthetic problems and theoretical costs of some real code examples.…”

“…Automatic array alignment has been intensively studied, and many heuristics have been proposed [4,11,17,24]. Implementation of these techniques in current array programming systems is not yet common.…”

“…If conflicts do exist, the goal is to find orientations that minimize the total cost of the communication overheads. A globally optimal solution is achieved by a perfect alignment of some spanning tree subgraph of the data flow graph [24]. The obvious heuristic is to maximize the length of the spanning tree [17] or, similarly, minimize the length of fundamental circuits [30], as this guarantees the alignment for the most expensive operations.…”

“…The alignment relationships for the derived operations in Fig. 2 and the alignment constraints posed by lower-level primitives spread and reduce are discussed in [24]. …”

“…If all the arrays are placed in the default norm orientation, residual communication is needed in all three assignments. A better placement can be devised by using the orientation preference graph [24], which is the data flow graph of the code with alignment preferences associated with its edges [17]. An alignment preference specifies the relationship between the variables corresponding to the endpoints of the edge.…”