Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
Is it possible to solve a problem of O(n!) complexity within a reasonable time given infinite number of processing units and infinite space?
The typical example of O(n!) problem is brute-force search: trying all permutations (ordered combinations).
It sure is. Consider the Traveling Salesman Problem in it’s strict NP form: given this list of costs for traveling from each point to each other point, can you put together a tour with cost less than K? With the new infinite-core CPU from Intel, you just assign one core to each possible permutation, and add up the costs (this is fast), and see if any core flags a success.
More generally, a problem in NP is a decision problem such that a potential solution can be verified in polynomial time (i.e., efficiently), and so (since the potential solutions are enumerable) any such problem can be efficiently solved with sufficiently many CPUs.