The new strategy tries to minimize the communication workload or latency during the shuffle phase, and it solves the problem based on the Linear Assignment Problem.

The FD assignment strategy in our work is a Linear Assignment Problem (LAP) which has been well studied in combinatorial optimization and linear programming.

(ii) Jonker and Volgenant algorithm [23]: A shortest augmenting path algorithm was developed to solve the Linear Assignment Problem.

The Linear Assignment Problem (LAP) is employed to find an optimal assignment which can minimize the communication workload.

In the first papers, it had been proved that in situ computations are always possible [4], that three types of assignments are sufficient to perform this kind of computations [5], that the length of in situ computations of mappings on [{0,1}.sup.n] is bounded by [n.sup.2] [6], and that any linear mapping on [{0,1}.sup.n] is computed with 2n--1 linear assignments [7].

Further work can also consist in improving bounds: for instance, it has been claimed very recently in [10] that the tight bound is [3.n/2j] linear assignments to compute linear mappings when S is the field Z/qZ for a prime power q (see also Open problem 1).