Kernel methods have been shown to be very effective for applications requiring the modeling of structured objects. However kernels for structures usually are too computational demanding to be applied to complex learning algorithms, e.g. Support Vector Machines. Consequently, in order to apply kernels to large amount of structured data, we need fast on-line algorithms along with an efficiency optimization of kernel-based computations. In this paper, we optimize this computation by representing set of trees by minimal Direct Acyclic Graphs (DAGs) allowing us i) to reduce the storage requirements and U) to speed up the evaluation on large number of trees as it can be done 'one-shot' by computing kernels over DAGs. The experiments on predicate argument subtrees from PropBank data show that substantial computational savings can be obtained for the perceptron algorithm.