Symmetry Robust Memory Management of Multidimensional Arrays

Abstract

Abstract Abstract In this paper we propose a simple strategy for memory management of multidimensional arrays whose entries are known to be invariant under a special permutation group P of the coordinates. The group P is not known in advance and is entered as a parameter of the procedure. The strategy is to obtain a partition of L δ n , the relevant lattice of positive integer points in R n , into parts which behaves well under the action of P. The partition is controlled by a hierarchy of combinatorial objects, forming a tree. The leaves of this tree are identified with some vertices of a digraph encoding special decreasing sequences. Both this digraph and the leaf-identified tree, denoted L δ n >P , are instances of Nijenhuis-Wilf combinatorial families. The members of L δ n /P become maximal paths in L δ n /P. This fact enables the quick computation of the address r δ p (δ), for δ ∈ L δ n /P .