Publisher's Synopsis
Excerpt from A Tight Lower Bound for the Complexity of Path-Planning for a Disc
Consider a fixed real number x; let i be an integer in the range 1 n. Then an (n, f) barrier around it is constructed as illustrated. The barrier has two connected components. Its center component is a rectangle of width 2, centered on the vertical line through x, with its y-coordinates between 1 and 3i] 1. The other component has y-coordinates between 4 and 3n+5, and is designed so that for the disc to pass the barrier it must negotiate a 'passage' around the center component, of width 3 units throughout, beginning with y-coordinate 4.
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