final(8) - CS 573 Final Exam Questions (December 17, 2008)...

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Unformatted text preview: CS 573 Final Exam Questions (December 17, 2008) Fall 2008 You have 180 minutes to answer all seven questions. Write your answers in the separate answer booklet. You can keep everything except your answer booklet when you leave. 1. An integer program is a linear program with the additional constraint that the variables must take only integer values. Prove that deciding whether an integer program has a feasible solution is NP-complete. [Hint: Almost any NP-hard decision problem can be formulated as an integer program. Pick your favorite.] 2. Recall that a priority search tree is a binary tree in which every node has both a search key and a priority , arranged so that the tree is simultaneously a binary search tree for the keys and a min-heap for the priorities. A heater is a priority search tree in which the priorities are given by the user, and the search keys are distributed uniformly and independently at random in the real interval [ 0,1 ] . Intuitively, a heater is the opposite of a treap. The following problems consider an n-node heater T whose node priorities are the integers from 1 to n . We identify nodes in T by their priorities; thus, node 5 means the node in T with priority 5. The min-heap property implies that node 1 is the root ofpriority 5....
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final(8) - CS 573 Final Exam Questions (December 17, 2008)...

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