Question

O: Naive algorithm coloring graphs: dild Engineering use the foll?2, is its complexity , vn) be colored with k colors? We pseudo-code. What (2 Pts) naïve algorithm in pseu Naive Algorithm: 1. Try all possible ways of assigning k colors to the n verticesTry to color V1, V2, Vn With the colors 1,2,,k. 2. If a valid coloring is found then answer is yes. Otherwise, answer is no. Complexity: O(2)

Answer 1

Since we have k-colors available for n vertices, and we need to color the vertices, the total complexity of this naive algorithm is O(k^n!).

This is because, we have to try out all the possible assignments of k colors to the n vertices. And since there all n! possible assignments, the total complexity becomes O(k^n!).