approximation algorithms guarantee: solution within factor α of optimal

Overlapping subproblems

Dynamic programming solves overlapping subproblems by storing results of subproblems to avoid redundant calculations

Convex optimization

Convex functions have only one global minimum

second-order methods (Newton's) converge faster but are expensive: O(n³) per step

Second-order methods converge faster due to quadratic convergence but are expensive due to O(n³) per iteration

Randomized algorithm

Randomized algorithms use random bits for expected polynomial time

UMAP is faster than t-SNE

UMAP is faster due to approximate nearest neighbors and cross-entropy optimization

Kolmogorov complexity

Kolmogorov complexity is uncomputable