Algorithm -- Monotone Decomposition -- Running Time

• initializing
• Q : O(n)
• T : O(1)
• total : O(n)
• handling an event
• one operation on Q : O(log n)
• at most one query, one insertion, and one deletion on T : O(log n)
• insert at most two diagonals into D : O(1)

                
• total : O(log n)
• total running time
• O(n log n)
• storage
• every vertex stored at most once in Q
• every edge stored at most once in T
• so, linear

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