JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 28, 313-325 (1969) Contribution to Nonserial Dynamic Programming* UMBERTO BERTEL~ AND FRANCESCO BRIOSCHI Istituto di Elettrotecnica ed Elettronica-Laboratorio di Controlli Automatici-Politecnico di Milano-Milano, Italy. Submitted by Richard Bellman A new property of nonserial dynamic programming is presented in this paper. This property allows cutting down considerably the com- putational effort required for solving the secondary optimization problem. 1. INTRODUCTION The application of the principle of optimality of dynamic programming to the solution of the problem of optimizing non serial systems has been widely discussed in the literature [I, 5-71. In this context the principle of optimality can conveniently be regarded as a decomposition technique which, at the cost of some (and often too much) storage, allows breaking the optimization problem in many smaller sub- problems. Two recent works [3, 41, deal with the problem of finding a decomposition which is optimal from the point of view of minimizing the number of opera- tions required with the constraint that the storage space does not exceed a prescribed level. This paper follows closely the approach of [3] and [4], and presents a new mathematical result, which has some important computational implications. The paper is organized in sections as follows. (a) Section 2 contains a short survey of those parts of [3] and [4] which are relevant to this work. (b) Section 3 presents a short example. (c) Section 4 introduces the definition of absence graph. (d) Section 5 contains the mathematical results of the paper. (e) Section 6 discusses some computational implications of the results of the preceeding section. Some elementary graph and set theory is used throughout the paper. An adequate reference is, for instance, Berge [2]. * This work has been supported by C.N.R. 313