Exact Analysis of Exact Change

We introduce the k-payment problem: given a total budget of N units, the problem is to represent this budget as a set of coins, so that any k exact payments of total value at most N can be made using k disjoint subsets of the coins. The goal is to minimize the number of coins for any given N and k, while allowing the actual payments to be made on-line, namely without the need to know all payment requests in advance. The problem is motivated by the electronic cash model, where each coin is a long bit sequence, and typical electronic wallets have only limited storage capacity. The k-payment problem has additional applications in other resource-sharing scenarios. Our results include a complete characterization of the k-payment problem as follows. First, we prove a necessary and sufficient condition for a given set of coins to solve the problem. Using this characterization, we prove that the number of coins in any solution to the k-payment problem is at least kHN/k, where Hn denotes the nt...

• Type: Conference
• Year: 1997
• Where: ISTCS
• Authors: Pat Frankel
• Keywords: Applied Computing, Coin, Exact Payments, ISTCS 1997, K-payment Problem