Homework problem L on Accelerated Binomial Heaps

Problem L

Assigned Oct 16+5, due Nov 4.

Accelerated Binomial Heaps

  1. (9 points) Construct a sequence of Binomial_Heap _Insert(), _Union(), and _Extract_Min() calls, including at least one _Extract_Min() call, such that the total number of Binomial_Link() calls made within the sequence is smaller for acceleratedBinomialHeaps than for binomialHeaps. For binomialHeap definitions use either CLR pseudocode or the code in binomialHeap.h. For acceleratedBinomialHeap definitions use binomialHeapA.h.

  2. (1 point) A sequence, s = s1, s2, ..., sn, is a basic binomial Heap sequence if each si is a call to one of the 4 basic binomial heap functions Binomial_Heap _Insert(), _Union(), _Minimum(), and _Extract_Min().
    Let Tstd(s) be the total time required for the calls in s if using the standard binomial heap implementation.
    Let Tacc(s) be the total time required for the calls in s using the accelerated binomial heap implementation.
    Let T(n) = max({Tstd(s)/Tacc(s) | s is a valid basic binomial heap sequence of length n}).
    Explain why T(n) is Ω(lg(n)).