This stems from the fact that finding all EMs that use a particular reaction is nondeterministic polynomial time

hard (NP-hard) [32]. 3.1. Deterministic and Non-Deterministic Polynomial Complexity In computational complexity theory [33,34], deterministic polynomial (P) and non-deterministic polynomial time (NP) are two classes of decision problems that classify computational problems according to their inherent difficulty in terms Inhibitors,research,lifescience,medical of their solvability by a computer. The selleck compound computation problem can be stated by a set of mathematical instructions consisting of problem instances and solutions to these problem instances. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantify the amount of resources needed to solve Inhibitors,research,lifescience,medical them, such as time and storage. One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do and the big O Inhibitors,research,lifescience,medical notation is useful for analyzing

the run time for class P and NP problems. The big O notation can analyze the efficiency of algorithms such as the time (T) (or the number of steps) it takes to complete a problem of size n. For example the Inhibitors,research,lifescience,medical time might be found to be T(n) = 6n2-2n+5. As n grows large, the n2 term will come to dominate, so that all other terms can be neglected. The coefficients also become irrelevant if T(n) is compared to other orders of expression Inhibitors,research,lifescience,medical e.g., n3 or n4; U(n) = n3, will always exceed T(n) when n gets larger than 6. The number of steps, on the other hand, depends on the details of the machine model on which the algorithm runs, although different types of machines generally vary by only a constant factor

in the number of steps needed to execute an algorithm. So the algorithm has order of n2 time complexity denoted by the big O as: (3) Note: The following two right-hand side big O notations have dramatically different meanings: (4) The first case states that f(m) exhibits polynomial growth, while the second, assuming m > 1, states that g(n) exhibits exponential growth. Megestrol Acetate Class P consists of those decision problems whose solution can be obtained using a deterministic algorithm that runs in polynomial time, i.e., runs in O(nk)steps for some non-negative integer k, where n is the input size. A deterministic algorithm only has one choice in each step taken to execute the problem, i.e., it would have the same output for every run on the same input instance for the problem.