Advanced algorithms: Assignment 2

Due: 2 Aug 2004

1. (10 points) The parallel algorithm for matrix-vector multiplication, based on a 2-dimensional decomposition, distributed the vectors b and c over the first colum of processors. Give an efficient parallel algorithm that distributes it over the first row of processors, and derive its time complexity.
2. (10 points) Give two algorithms for matrix-vector multiplication, one which has a cache complexity of O(n²) and another that has a cache complexity of O(n²/L), under the ideal cache model that we discussed.
3. (10 points) Show how the randomized quicksort algorithm sorts the input 8, 7, 6, 5, 4, 3, 2, 1, given a floating point random number sequence 0.5, 0.25, 0.75, 0.3, 0.1, 0.9, 0.8, 0.6.
4. (20 points) Given the following points: P = {(1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3)}, show the composite numbers that correspond to this, and construct a layered range tree from the composite numbers. Then show how this tree is used to search for all points in the region: x = 0.9, x' = 2.1, y = 2, y' = 3.