Generalized Minimum Cost Flow and Arbitrage in Bitcoin Debit and Custodian Networks

Abstract

This project was focused on designing a tool for optimizing complex transactions in a traditional bank accounts, Bitcoin wallet accounts and Bitcoin exchanges. The challenges include transference fees eroding the amounts transferred, Bitcoin volatility and arbitrage. The tool should support hundreds of accounts with each account identifi ed by a bank or exchange, and a currency. The basic user-case, we call it Debit Scenario, appears when an account consumes it capital and has very little funding (sink or demand account), then the user set a minimum funding for the account, and we need to balance all the accounts of the network, using many currency circulations though many paths to satisfy the specifi ed funding limits. Another user case, we called it Custodian Scenario, is when certain accounts (i.e. supply or non-custodians) has upper limit on the amount of capital so we need to distribute the excess value in other accounts (i.e. demand or custodians) of the network. The problem was modelled as a multi-commodity min-cost max- flow problem with specifi c constraints including arbitrage information, and solved with linear programming. Simple and complex numerical scenarios are presented too.