Bartering leftovers on the internet

This work promotes the idea of using special software allowing Internet users to exchange "leftovers", namely goods with no monetary value except for the possibility of exchanging them with other leftovers. We show how to automate such an activity. We first study the problem of defining the notion of "market clearing" in bartering leftovers as is done in 2x ₁+3x₃ and general Exchange systems. We formally define the relevant optimization problem (called IBP) of maximizing the number of useful exchanges between a set of users. We show that the general problem is NP hard. We consider a restricted case of IBP where each user has one exchange wherein exactly k unique goods are to be exchanged. We show that this can be solvable in polynomial times via a reduction to a Network Flow problem. Due to natural need of building a peer-to-peer bartering system we design a practical protocol for bartering leftovers allowing (unlike the algorithm for the restricted case) a highly distributed peer-to-peer implementation. In particular, this protocol help users to learn different combinations of goods to be exchanged thus increasing the number of successful exchanges.