Pin Assignment

Abstract

The previous chapter dealt with determining optimal paths for droplets in order to realize experiments. As reviewed in Chap. 1, droplets are moved by actuating the electrodes underneath the cells. Biochips with hundreds of cells, see, for example (Zhao and Chakrabarty, IEEE Trans Comput Aided Des Integr Circuits Syst 31(2):242–254, 2012), pose a serious problem for the physical realization of the connection between the cells and the corresponding control logic. The core problems are that micro-controllers usually do not have up to thousand output pins and that the wire routing on the PCB becomes infeasible. To overcome this problem, the idea is to drive multiple electrodes by the same control signal. The process of assigning control signals to electrodes is known as pin assignment. Obviously, the pins that are assigned to electrodes must be chosen carefully as their actuation must still lead to the same droplet movements. This chapter will deal with the question of how to divide the electrodes into as few groups as possible that still allow to realize the intended movements of droplets when all electrodes in a group are actuated the same way. In Sect. 4.1, the problem is formally defined. Afterwards, in Sect. 4.2, it is proven that the problem of minimizing the number of pins is N P-complete. Section 4.3 reviews related work. Then, two different algorithms for determining such an assignment are presented in Sect. 4.4: one heuristic framework and one exact algorithm. Experimental results are presented in Sect. 4.5.