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Unformatted text preview: Massachusetts Institute of Technology Handout 2 6.854J/18.415J: Advanced Algorithms Wednesday, September 9, 2009 David Karger Problem Set 1 Due: Wednesday, September 16, 2009. Collaboration policy: collaboration is strongly encouraged . However, remember that 1. You must write up your own solutions, independently. 2. You must record the name of every collaborator. 3. You must actually participate in solving all the problems. This is difficult in very large groups, so you should keep your collaboration groups limited to 3 or 4 people in a given week. 4. No bibles. This includes solutions posted to problems in previous years. NONCOLLABORATIVE Problem 1. Unlike regular heaps, Fibonacci heaps do not achieve their good performance by keeping the depth of the heap small. Demonstrate this by exhibiting a sequence of Fibonacci heap operations on n items that produce a heap-ordered tree of depth ( n ). Problem 2. Suppose that Fibonacci heaps were modified so that a node was cut only after losing k children. Show that this will improve the amortized cost of decrease key (to a better constant) at the cost of a worse cost for delete-min (by a constant factor).better constant) at the cost of a worse cost for delete-min (by a constant factor)....
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- Fall '09