CSE101Finals-VersionASolution.pdf

# CSE101Finals-VersionASolution.pdf - a Algorithm 1.,li...

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a) Algorithm: 1. Sort the given set of technologies by low frequency, l i . 2. While [L, H] is not covered, repeat: Proceed along the list of intervals, and find the technology T i with interval [l i , h i ] such that l i ≤ L and h i is the maximum of all the intervals with l i ≤ L. Select technology T i , and discard all other technologies T j with l j ≤ l i . So in words, the technology is selected based on two conditions: that it is able to cover a frequency sub­interval, which starts at or before the end of the frequency interval of the previous chosen technology, and whose frequency sub­interval end is the farthest along the spectrum. b) Proof: Consider the set S of all the intervals of the technologies chosen by the greedy solution, and let OPT be an optimal solution, with all intervals also ordered in increasing order of l i . Consider the first interval in both solutions. Replacing the first interval in OPT, (l OPT , h OPT ) with the first interval from S, (l S , h S ) , which has the farthest right endpoint, h

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