On approximating the memory-Constrained Module Allocation Problem - Roupin, Frédéric (Information processing letters, 1997)
In this paper, we consider a variant of the module allocation problem in a distributed system, where processors have limited memory (memory-Constrained Module Allocation Problem). This problem consists of assigning N modules to P processors in order to minimize the sum of execution times and communication costs. We show that even in three simplified cases, unless P = NP, no polynomial-time algorithm can guarantee to find a feasible solution within c percent of the optimal value, where c is any fixed positive constant. One of these particular cases is the minimization version of the k-partition problem.