An iteration is one repetition of an algorithmic cycle or update sequence. In k-means, the main cycle runs up to a chosen maximum number of iterations, m; in simulated annealing, iterations attempt updates, while temperature may change only after an interval. section 12.2.3 section 17.1.4
Iteration counts affect both runtime and search behavior. For k-means with n points, k clusters, and d dimensions, the stated running time is O(m*k*n*d). In simulated annealing, pure random steps may need many iterations; balancing small steps with occasional long-range updates offers another approach. section 12.2.3 section 17.1.4
