  Payment channel is a protocol which allows cryptocurrency users to route
multiple transactions through network without committing them to the main
blockchain network (mainnet). This ability makes them the most prominent
solution to blockchains' scalability problem. Each modification of payment
channels requires a transaction on the mainnet and therefore, big transaction
fees. In this paper, we assume that a set of payment transactions are given
(batch or online) and we study the problem of scheduling modificiations on
payment channels to route all of the transactions with minimum modification
cost.
  We investigate two cost models for aforementioned problem: the step cost
function in which every channel modification has a constant cost and the linear
cost function in which modification costs are proportional to the amount of
change. For the step cost function model, we prove impossibility results for
both batch and online case. Moreover, some heuristic methods for the batch case
are presented and compared. For the linear cost we propose a polynomial time
algorithm using linear programming for the batch case.
