Dynamic Programming: Bellman-Ford and Dijkstra

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Covers the implementation and analysis of disjoint sets data structure and introduces the concept of minimum spanning trees.

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

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Discusses variance reduction techniques in stochastic simulation, focusing on allocation strategies and replica generation algorithms.

Introduces the concept of shortest path, discussing weighted paths, Hamiltonian paths, and path optimization algorithms.

Covers Dijkstra's algorithm and its application to the all-pairs shortest path problem.

Explores choosing a step size in optimization on manifolds, including backtracking line-search and the Armijo method.

Covers the Newton's local method in Python using NumPy for optimization.

Explores GPU-accelerated join order optimization in large search spaces, leveraging graph topology to reduce computational overheads.