CS531 Final Exam Winter, 1998 This exam is closed book . Answer all questions in the blue books. Unsupported work will receive no credit. 1. (10%) Prove that 1 1 k n k n = ∑ = Θ (log ). 2. (10%) Draw an 8-element bitonic sort unit. 3. Given a set of n integer values in the range of [1,100], for each of the following architectures, give an efficient algorithm to sort these data items. Discuss the quality of each of your solutions in terms of time/space/processors. a) (10%) RAM b) (10%) PRAM 4. Define a Reconfigurable Array of size n to be a linear array augmented by a reconfigurable bus . The reconfigurable bus has the characteristic that every processor has the ability to split or connect the bus between itself and either (or both or neither) of its neighbors during every step of an algorithm . That is, the bus can be dynamically reconfigured on the fly. Further, on each bus segment, only 1 processor can perform a write and all processors can read the value written (i.e., the bus is CREW within each independent segment).
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