What are some strategies to the game of Flow?
Flow is an iDevice app that seems to be pretty popular recently. The game board is a square array of cells, with several pairs of colored endpoints. The goal is to connect all of the endpoints with lines, and the lines cannot overlap and must fill the entire board. Here and here are photos of the game near completion. These are examples on a small game board, but the boards can get up to 14×14 in size with more than a dozen colors of line.
This game seems as if it ought to have some sort of underlying strategy. What strategy could there be?
This question is in the General Section. Responses must be helpful and on-topic.