Comments on: What are P, NP-Complete, and NP-Hard? http://explorations.chasrmartin.com/2008/11/24/what-are-p-np-complete-and-np-hard/ Believe nothing, no matter where you read it, or who said it, unless it agrees with your own reason and your own common sense. Fri, 08 Jan 2010 20:08:57 +0000 http://wordpress.org/?v=2.9.2 hourly 1 By: Charlie http://explorations.chasrmartin.com/2008/11/24/what-are-p-np-complete-and-np-hard/comment-page-1/#comment-2352 Charlie Tue, 29 Dec 2009 18:33:13 +0000 http://explorations.chasrmartin.com/?p=1549#comment-2352 Ooh, excellent question. Steve Cook was the first person to define NP-complete problems, and you're exactly right. What Cook's theorem originally said was that there exists a class of problems which are (1) in NP, and (2) which can be reduced in polynomial time to an instance of <a href="http://en.wikipedia.org/wiki/Boolean_satisfiability_problem" rel="nofollow">boolean satisfiability</a>. So this definition can be restated as defining the class of problems which are in NP and which are reducible to boolean satisfiability. Since polynomial-time reducibility is closed under composition — that is, if X is poly-time and Y is poly-time, the Y(X) is also poly-time — all that's necessary to prove any particular problem is in the class is to show that the problem is in NP and can be reduced in poly-time to any known NP-complete problem. Ooh, excellent question. Steve Cook was the first person to define NP-complete problems, and you’re exactly right. What Cook’s theorem originally said was that there exists a class of problems which are (1) in NP, and (2) which can be reduced in polynomial time to an instance of boolean satisfiability. So this definition can be restated as defining the class of problems which are in NP and which are reducible to boolean satisfiability. Since polynomial-time reducibility is closed under composition — that is, if X is poly-time and Y is poly-time, the Y(X) is also poly-time — all that’s necessary to prove any particular problem is in the class is to show that the problem is in NP and can be reduced in poly-time to any known NP-complete problem.

]]> By: tomerbd http://explorations.chasrmartin.com/2008/11/24/what-are-p-np-complete-and-np-hard/comment-page-1/#comment-2351 tomerbd Tue, 29 Dec 2009 18:16:30 +0000 http://explorations.chasrmartin.com/?p=1549#comment-2351 A problem is NP-complete if you can prove that (1) it’s in NP, and (2) show that it’s poly-time reducible to a problem already known to be NP-complete. didn't you just put inside the definition of NP-Complete the term itself to define? inside the definition you use NP-Complete, so what is the first NP-Complete problem? A problem is NP-complete if you can prove that (1) it’s in NP, and (2) show that it’s poly-time reducible to a problem already known to be NP-complete.

didn’t you just put inside the definition of NP-Complete the term itself to define? inside the definition you use NP-Complete, so what is the first NP-Complete problem?

]]> By: NP, Medical Dictionary & A Place to Bury Strangers links for 2008-12-02 - WebliminalBlog http://explorations.chasrmartin.com/2008/11/24/what-are-p-np-complete-and-np-hard/comment-page-1/#comment-2292 NP, Medical Dictionary & A Place to Bury Strangers links for 2008-12-02 - WebliminalBlog Mon, 08 Jun 2009 01:15:51 +0000 http://explorations.chasrmartin.com/?p=1549#comment-2292 [...] What are P, NP-Complete, and NP-Hard? | Explorations We start with the idea of a decision problem, a problem for which an algorithm can always answer “yes” or “no.” We also need the idea of two models of computer (Turing machine, really): deterministic and non-deterministic. A deterministic computer is the regular computer we always thinking of; a non-deterministic computer is one that is just like we’re used to except that is has unlimited parallelism, so that any time you come to a branch, you spawn a new “process” and examine both sides. Like Yogi Berra said, when you come to a fork in the road, you should take it. (tags: np-complete np-hard) [...] [...] What are P, NP-Complete, and NP-Hard? | Explorations We start with the idea of a decision problem, a problem for which an algorithm can always answer “yes” or “no.” We also need the idea of two models of computer (Turing machine, really): deterministic and non-deterministic. A deterministic computer is the regular computer we always thinking of; a non-deterministic computer is one that is just like we’re used to except that is has unlimited parallelism, so that any time you come to a branch, you spawn a new “process” and examine both sides. Like Yogi Berra said, when you come to a fork in the road, you should take it. (tags: np-complete np-hard) [...]

]]> By: WebliminalBlog » Blog Archive » links for 2008-12-02 http://explorations.chasrmartin.com/2008/11/24/what-are-p-np-complete-and-np-hard/comment-page-1/#comment-2212 WebliminalBlog » Blog Archive » links for 2008-12-02 Tue, 02 Dec 2008 11:30:12 +0000 http://explorations.chasrmartin.com/?p=1549#comment-2212 [...] What are P, NP-Complete, and NP-Hard? | Explorations We start with the idea of a decision problem, a problem for which an algorithm can always answer “yes” or “no.” We also need the idea of two models of computer (Turing machine, really): deterministic and non-deterministic. A deterministic computer is the regular computer we always thinking of; a non-deterministic computer is one that is just like we’re used to except that is has unlimited parallelism, so that any time you come to a branch, you spawn a new “process” and examine both sides. Like Yogi Berra said, when you come to a fork in the road, you should take it. (tags: np-complete np-hard) [...] [...] What are P, NP-Complete, and NP-Hard? | Explorations We start with the idea of a decision problem, a problem for which an algorithm can always answer “yes” or “no.” We also need the idea of two models of computer (Turing machine, really): deterministic and non-deterministic. A deterministic computer is the regular computer we always thinking of; a non-deterministic computer is one that is just like we’re used to except that is has unlimited parallelism, so that any time you come to a branch, you spawn a new “process” and examine both sides. Like Yogi Berra said, when you come to a fork in the road, you should take it. (tags: np-complete np-hard) [...]

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