The Team USA Winter Olympic 5-Person Snowball Throwing Trials are approaching. There are n coaches available; each will coach a single 5-Person Snowball Throwing Team (“5PSTT” for short). 5n athletes are eagerly competing for these highly coveted 5PSTT slots. After practices, trials and training, each athlete ranks the n coaches, and each coach ranks all 5n athletes. A “stable team assignment” assigns 5 athletes to each coach so that no coach c is assigned and athlete a who would prefer a different coach c 0 and simultaneously c 0 is assigned an athlete a 0 who prefers coach c. This is similar, but not identical, to the Stable Matching Problem (SMP). Explain how you could use, without modification, a subroutine that solves SMP to solve the Stable 5PSTT Problem (S5PSTTP). I.e., explain how to transform an S5PSTTP instance x into an SMP instance f(x) in such a way that any stable solution to the SMP instance f(x) can be easily converted into a stable solution to the S5PSTTP instance x. I’m looking for about 3 clear, English language, paragraphs explaining (1) how to convert x to f(x) (2) how to recover a solution to the S5PSTTP instance x from a Stable Matching found in f(x), and (3) explaining why that result is actually a “stable team assignment”. I expect that your solution would require O(n) time, excluding the time taken by the SMP subroutine; briefly justify this (if true), or explain why your method may be slower

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To solve the Stable 5Person Snowball Throwing Team Problem S5PSTTP using a subroutine that solves the Stable Matching Problem SMP we can perform a sim... View the full answer