Unformatted text preview: Prove that not both these operations can be done in o (log n ) time even if amortization is allowed. 4. Consider the cut operation in Fibonacci heaps. In the usual implementation, a node is cut as soon as it loses two of its children. Let’s change this rule: a node is cut as soon as it loses three of its children. Analyse this variant of Fibonacci heap. Is MaxDeg ( n ) still O (log n )? 5. In next class, we’ll show that insertions in redblack trees cost 2 rotations (case 2) and upto O(log n) color changes (case 1). Show that amortized color updates per insertion is O(1). (Hint: to develop an appropriate potential function try to see what is decreasing in the structure when we push the redconﬂict upwards in case 1.) 1...
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 Spring '11
 r
 Algorithms, Array data structure, Fibonacci heap, Priority queue, Persistent data structure

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