FSPMs make intensive use of algorithms that manipulate the branching structure of plants. These algorithms may serve a variety of computational purposes related to these branching structures such as displaying them on screen, extracting data samples and statistics from them, comparing them, computing flows of matter (water, nutrients, signals) through them, computing the propagation of physical forces in them, or growing them. In general, the computational complexity of all these algorithms is directly proportional to a power (greater than 1) of the number N of components of the considered branching structure. In most FSPMs, N is relatively high and tends to grow exponentially with the plant's age, at least in the first stages of plant development. For this reason, most FSPM algorithms are computationally expensive, with a time and memory complexity at least proportional to N. Different strategies have been considered to reduce this computational complexity and they most of them make use of a change of scale in the plant representation. Rather than computing light interception on each leaf of a tree for example, more efficient algorithms can be achieved by assessing the light intercepted by crownlets at a coarser scale. These approaches are computationally efficient but require both a change of plant representation and of the associated models. In this paper, we present a new way of reducing algorithm complexity in FSPMs by compressing plant branching structures representation at a given scale. For this, we make use of the possibility to compress tree branching structures as directed acyclic graphs (DAGs) either in a lossless or approximate manner. We show how these DAG-transforms of branching systems can be used to reformulate a wide class of algorithms that operate on trees, and that, if N denotes the number of tree components and D the number of DAG components corresponding to the compressed tree, the algorithm complexity are in general reduced from O(N) to O(D)