Algorithm -- Monotone Decomposition -- Eliminating Merge Vertices

• for a merge vertex v_i, let e_j be the edge immediately to the left of it
• v_i becomes helper(e_j) once we reach it
• whenever the helper(e_j) is replaced by some vertex v_m, add a diagonal from v_m to v_i
• if v_i is never replaced as helper(e_j), we can connect it to the lower endpoint of e_j

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