Topic Questions Sorting Circuit Permutation Circuits 1. (a) In Akl, chapter 3.1 (step 2, p. 103), we are given a proof of why ui+1 > z2i, where ui are the odd-indexed elements of the two input sequences. Prove that this is also true for vi the even-indexed inputs, i.e., vi > z2i. (b) In step 3, we are given a proof of why z2i+1 > ui+1. Similarly, prove that z2i+1 > vi. 2. Explain why self-routing circuits are ill-suited to the task of permutation. Prefix Sum Circuits, Prefix Computation (PRAM) Searching 1. Problem 4.5(c): Show how the prefix computation over x0, x1, â€¦ , xn-1 can be performed on a mesh with n1/2 x n1/2 processors. 2. Can one search for an item in O(1) time using n1/2 processorsin an array of n sorted items? General Prefix Computation Merging 1. Is General Prefix Computation harder than sorting? 2. What is the time complexity of the optimal merging algorithm in 5.2.5? Selection Convex Hull 1. Problem 5.16, p.227: Show how algorithm PRAM SELECT can be used to derive a parallel algorithm for sorting on the PRAM a sequence of numbers given in arbitrary order. 2. Problem 5.20, p.228: Design a parallel divide and conquer algorithm for determining whether any two of n given straight- line segments in the plane intersect. Pointer Jumping & Linked List Ranking Euler Tour 1. Problem 6.2, p.265: In section 6.2, prior to executing algorithm PRAM LINKED LIST PREFIX, those processors involved in performing the prefix computation over L can determine their number (and hence the number of nodes in L) by writing a 1 in a location size of memory, using a SUM CW. 1 1/25/2016 11:01 AM Discuss how this information can be used to provide an alternative termination condition for the algorithm. 2. Give an algorithm for numbering the nodes of a tree in in- order traversalsequence. The assumptions of the Euler Tour algorithm hold. Also, assume that if there are k children of a node v, then v is visited after its first child and its descendants are visited.
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