Memory minimization for tensor contractions using integer linear programming

This paper presents a technique for memory optimization for a class of computations that arises in the field of correlated electronic structure methods such as coupled cluster and configuration interaction methods in quantum chemistry. In this class of computations, loop computations perform a multi-dimensional sum of product of input arrays. There are many different ways to get the same final results that differ in the required number of arithmetic operations required. In addition, for a given number of arithmetic operations, different expressions of the loop have different memory requirements. Loop fusion is a plausible solution for reducing memory usage. By fusing loops between producer loop nest and consumer loop nest, the required storage of intermediate array is reduced by the range of the fused loop. Because resultant loops have to be legal after fusion, some loops can not be fused at the same time. In this paper, we have developed a novel integer linear programming (ILP) formu...

• Type: Conference
• Year: 2006
• Where: IPPS
• Authors: A. Allam, J. Ramanujam, Gerald Baumgartner, P. Sadayappan
• Keywords: Distributed And Parallel Computing, IPPS 2006, Loop, Loop Fusion, Loop Nest