MIT1_204S10_assn4

MIT1_204S10_assn4 - 1.204 Computer Algorithms in Systems...

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1.204 Computer Algorithms in Systems Engineering Spring 2010 Problem Set 4: Satellite data sets Due: 12 noon, Monday, March 29, 2010 1. Problem statement You receive data from a series of satellites on cloud cover and atmospheric temperatures on a near-real-time basis. Each satellite transmits a series of data points, represented as an array, for the areas it can observe. There are multiple satellites; sometimes their measurement areas overlap, and sometimes there are gaps. To simplify the problem, we will assume that the data can be sorted by one dimension (longitude) instead of two (latitude and longitude). The satellites report their data at approximately the same time, and you must merge all the data you receive into a single array, sorted by longitude. The order in which the satellites report appears random. They all report within a few seconds or even milliseconds of each other, but the order is essentially unpredictable since it’s based on their distance from the ground station, the processing time on the satellite to compute the measurements and the number of measurements to transmit. This is a common problem in monitoring and analyzing sensor data. To solve it, you will implement an optimal merge algorithm as outlined in the Horowitz text in section 4.7. 2. Algorithm a. Merging two arrays Section 3.4 in the textbook describes the mergesort algorithm, which recursively sorts an array. The mergesort algorithm uses a helper algorithm, called merge, which is used for merging two sorted subsets of an array. This is similar to how quicksort uses partition. The merge algorithm works as follows. Initially, you have two indexes pointing to the 0 th elements of both arrays. These are the smallest elements in both the arrays as they are sorted. You then choose the smaller of these two elements and this is the 0 th element in the new (result) array. You then update the index in the array from which you have chosen the 0 th element to the next element (1 st element) and again compare the elements to fill the 1 st position in the sorted array. At each step, you compare the smallest element in the two arrays and choose the smaller of them to fill the new array and update the indexes accordingly until you fill the new array completely.
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As an example, consider the two arrays: {1,4,7} and {2,3,5}, which are sorted and have to be merged into a single sorted array. The size of this sorted array is 6 (3+3). The figure below shows how the merge operation works for these two arrays. The two arrays are represented vertically. The vertical lines separate the successive steps in the merge algorithm. The circles represent the indexes. At each step of the algorithm, you compare two elements (pointed to by the indexes) and choose the smaller of them to fill in the new array. 2
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MIT1_204S10_assn4 - 1.204 Computer Algorithms in Systems...

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