Why connectedness is hard to compute
• Even for simple line drawings, there are
exponentially many cases.
• Removing one segment can break
connectedness
– But this depends on the precise
arrangement of the other pieces.
– Unlike parity, there are no simple
summaries of the other pieces that tell
us what will happen.
• Connectedness is easy to compute with an
iterative algorithm.
– Start anywhere in the ink
– Propagate a marker
– See if all the ink gets marked.