Memory size bounds of prefix DAGs

In this report an entropy bound on the memory size is given for a compression method of leaf-labeled trees. The compression converts the tree into a Directed Acyclic Graph (DAG) by merging isomorphic subtrees. I. COUPON COLLECTOR’S PROBLEM WITH ARBITRARY COUPON PROBABILITIES Given a set of C coupons, where δ = |C| denotes the number of coupons. At each draw po denotes the probability for getting coupon o for o ∈ C. We draw m coupons, and let E denote the expected number of different coupons we have obtained. The task is to give an upper bound on E. Let V denote the set of coupons we have after m draw. The probability of having coupon o in V is P (o ∈ V ) = 1− (1 − po) m (1) Thus the expected cardinality of V is E(|V |) = ∑