Aggregability is NP-Hard

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Max Shpak, The University of Texas at El PasoFollow

Publication Date

7-2006

Comments

UTEP-CS-06-29.

Published in ACM SIGACT News,, 2006, Vol. 37, No. 3, pp. 97-104.

Abstract

Many dynamical systems are aggregable in the sense that we can divide their variables x1,...,xn into several (k) non-intersecting groups and find combinations y1,...,yk of variables from these groups (macrovariables) whose dynamics depend only on the initial values of the macrovariables. For very large systems, finding such an aggregation is often the only way to perform a meaningful analysis of such systems. Since aggregation is important, researchers have been trying to find a general efficient algorithm for detecting aggregability. In this paper, we show that in general, detecting aggregability is NP-hard even for linear systems, and thus (unless P=NP), we can only hope to find efficient detection algorithms for specific classes of systems. We also show that in the linear case, once the groups are known, it is possible to efficiently find appropriate combinations ya.