Advanced Analysis of Algorithms - Homework III (Solutions)
نویسنده
چکیده
Solution: Yes; for instance consider the language L = {5}, i.e., the language containing a single element and the corresponding decision problem: D1: Does x ∈ L?. I can reduce an arbitrary decision problem D2 ∈ P to D1 using the reduction f , which is defined as follows: Given x as input to D2, f first checks in polynomial time, whether x ∈ D1. If x is a “yes” instance of D2, f(x) = 5; otherwise f(x) = 6. It is not hard to see that an instance x is a “yes” instance of D2 if and only if f(x) is a “yes” instance of D1! In other words, we have reduced D2 to D1. 2
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Advanced Analysis of Algorithms - Homework II (Solutions)
1. Problem 15-2 on Page 364 of [CLRS01]. Solution: Assume that the optimal solution packs the n words in r lines; this solution can be decomposed into two parts, viz., the words packed on the first line and the words packed in the remaining (r − 1) lines. Regardless of the choice for the last word on line 1, the remaining words must be packed optimally in the lines 2 through (r − 1). (Why?) We ...
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