Motivated by a problem in the theory of randomized search heuristics, we give a very precise analysis for the coupon collector problem where the collector starts with a random set of coupons (chosen uniformly from all sets). We show that the expected number of rounds until we have a coupon of each type is nHn/2 − 1/2± o(1), where Hn/2 denotes the (n/2)th harmonic number when n is even, and Hn/2...

A standard combinatorial problem is to estimate the number (T ) of coupons, drawn at random, needed to complete a collection of all possible m types. Generalizations of this problem have found many engineering applications. The usefulness of the model is hampered by the difficulties in obtaining numerical results for moments or distributions. We show two computational paradigms that are well su...

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 gettin...

A multi-coupon (MC ) represents a collection of k coupons that a user can redeem to a vendor in exchange for some goods or services. Nguyen (FC 2006), deepening the ideas of Chen et al. (FC 2005), introduced an unforgeable privacy-protecting MC system with constant complexity for issuing and redemption of MCs, that discourages sharing of coupons through a property called weak unsplittability, w...

We study Structured Coupon Collection, a problem introduced by Adler et al [AHKV03] in STOC 2003, over n/b disjoint cliques with b nodes per clique. Nodes are initially uncovered. At each step, we choose d nodes independently and uniformly at random. If all the nodes in the corresponding cliques are covered, we do nothing. Otherwise, from among the chosen cliques with at least one uncovered nod...

We consider the problem of identifying endogenous current coupons for To-BeAnnounced (TBA) agency mortgage pass through securities. Current coupons play a crucial role in the mortgage backed securities. The current coupon is said to be endogenous if it gives rise to a fairly, or par valued, TBA. Since prepayments both affect the value of the mortgage and depend heavily upon the coupon, the iden...

This paper discusses the use of parametric models for the term structure of interest rates and their uses. The paper focuses initially on a potential problem which arises out of the use of certain models. In most cases the process of parameter estimation involves the minimization or maximization of a function (for example, least squares or maximum likelihood). In some cases this function can ha...