DOUGLAS PUECKER HEURISTIC

• Given L=(p₁,...,p_n) and eps>0, find a decimated eps-approximation.
• ALGORITHM:
  - If (p₁,p_n) is admissible, done.
  - Else, find p_i of maximum distance.
  - Recursively, solve for (p₁,p_i) and (p_i,p_n).
• Simple and widely used.
• Heuristic because no guarantees.
• Implementation: naively, Theta(n²).
• Hershberger and Snoeyink:
  - O(nlogn) if use path hulls.
  - O(nlog^* n) if use bead hulls.
• Binary Line Generalization (BLG) Trees
  - from van Oosterom and van den Bos
  - store the Douglas-Puecker construction in a binary tree.
  - Each node i stores the distortion eps_i.
  - Can generate any eps-approximation by traversal of tree (do not go below node with distortion less than eps)