In this paper, we use crossing number and wire area arguments to find lower bounds on the layout area and maximum edge length of a variety of computationally useful networks. In particular, we describe 1) an N-node planar graph which has layout area Θ(NlogN), and maximum edge length Θ(N1/2/log1/2N), 2) an N-node graph with an O(N1/2)-separator which has layout area Θ(Nlog2N) and maximum edge length Θ(N1/2logN/loglogN), and 3) an N-node graph with an O(N1-1/r)-separator which has maximum edge length Θ(N1-1/r) for any r ≥ 3.
['Frank Thomson Leighton']
New lower bound techniques for VLSI