
In
recent years, many different cryptocurrencies have risen in popularity.
Since coins vary in fiat value and functionality, it has become
important to securely exchange between them. A common exchange method
is hashed timelock contracts (HTLC). However, this method did not
support brokerage transactions that allow parties to leverage assets
they gain during the transaction. We consider HTLC with brokering. The
transaction fees for HTLC is a direct function of the size of the
leader set. Thus, brokers are interested in finding the minimum leader
set of a given transaction graph. We show that finding the minimum
leader set on general transaction graphs with brokering is NPhard. We
then introduce flower transaction graphs, a common type of transaction
graphs with brokering, and show that finding the minimum leader set of
a flower graph is also NPhard through a reduction from the knapsack
problem.

