CS 1501 Lecture Notes - Lecture 11: Nondeterministic Algorithm, Time Complexity, Search Algorithm

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17 Nov 2016
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Cs 1501 11-16: so(cid:373)e pro(cid:271)le(cid:373)s are unsolvable: example is halting problem, halt test retur(cid:374)s true if it halts, intractable problems take a long time to solve but are solvable so are impractical even for modest input sizes ex. Listing all subsets of a set takes o(2^n); ex. I(cid:374)(cid:272)orre(cid:272)t optio(cid:374)s: p a(cid:374)d (cid:374)p (cid:272)a(cid:374)"t (cid:271)e (cid:272)o(cid:373)pletel(cid:455) i(cid:374)depe(cid:374)de(cid:374)t; p and np cannot have a. So nondeterministic algorithms can solve deterministic ones but not vice versa. Goal: show that my problem can be used to solve an np-complete problem and that. >polynomial runtime for these 2 the transformation of problem inputs can be performed in polynomial time: example of using reduction to show np-completeness: Npc(input) runtime for this is sum of the three steps below; takes exponential time o(2^n) Np = runtime(input newinput) + runtime(newprob) + runtime(newoutput output: e(cid:454)a(cid:373)ple (cid:1006): O(n) =output newoutput overall runtime must be exponential: o(2^n) =o(n+?+n)=o(?: e(cid:454)a(cid:373)ple (cid:1007)(cid:894)spe(cid:272)ifi(cid:272)(cid:895):

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