Omega polynomial function

Table 11.2 Omega polynomial in Diamond Dg and Lonsdaleite Lg nets, function of the number of repeating units along the edge of a cubic (k,k,k) domain Network... 

Table 11.7 Omega polynomial in D5 28 co-net function of = no. ada 20 units along the edge... 

Table 11.9 Omega polynomial in Lonsdaleite-like L5 28 and L5 20 nets function of k = no. repeating units along the edge of a cubic jk,k,k) domain...

The omega notation is used to provide a lower bound, while the theta notation is used when the obtained bound is both a lower and an upper bound. The little oh notation is a very precise notation that does not find much use in the asymptotic analysis of algorithms. With these additional notations available, the solution to the recurrence for insertion and merge sort are, respectively, 0(n ) and 0(n logn). The definitions of O, 2, 0, and o are easily extended to include functions of more than one variable. For example, f(n,m) = 0(g(n, m)) if there exist positive constants c, uq and mo such that /(n, m) < cg(n, m) for all n> no and all m > mo. As in the case of the big oh notation, there are several functions g(n) for which /(n) = Q(g(n)). The g(n) is only a lower bound on f(n). The 0 notation is more precise that both the big oh and omega notations. The following theorem obtains a very useful result about the order of f(n) when f(n) is a polynomial in n. 

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See also in sourсe #XX -- [ , ]

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