Hirschberg's Algorithm on a GCA and Its Parallel Hardware Implementation

We present in detail a GCA (Global Cellular Automaton) algorithm with 3n cells for Hirschberg’s algorithm which determines the connected components of a n-node undirected graph with time complexity O(n log n). This algorithm is implemented fully parallel in hardware (FPGA logic). The complexity of the logic and the performance is evaluated and compared to a former implementation using n(n+1) cells with a time complexity of O(log(n)). It can be seen from the implementation that the presented algorithm needs significantly fewer resources (logic elements times computation time) compared to the implementation with n(n+ 1) cells, making it preferable for graphs of reasonable size.