The new algorithm checks planarity in a number of steps proportional to the cube of the logarithm of the number of nodes in the graph — an exponential improvement. Holm and Rotenberg, a computer ...

Since the 1970s, algorithms have been able to test graph isomorphism, but in exponential time. This means that the increasing complexity of the graphs increased the algorithm's running time ...

The important insight is that for repetition codes, this results in what's called a planar graph, where edges don't cross each other. "This allows us to exploit the exact, efficient solutions for ...