Network Flows with Capacities: Revisited

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Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Cutset Formulation: MST Problem

Explores the cutset formulation for the MST Problem and Gomory Cutting Planes method.

Network Flows and LP Formulations

Explains network flows, LP formulations, simplex method, duality, and practical applications.

Integer Programming and Network Flows

Covers the fundamentals of integer programming and network flows in directed graphs.

Simplex Algorithm: Basics

Introduces the Simplex algorithm for solving flow problems and handling negative cost cycles.

Branch and Bound: Heuristic Maximization

Explains the Branch and Bound algorithm for heuristic maximization problems using LP relaxations and pruning techniques.

Solving Integer Linear Programs

Covers solving integer linear programs graphically, algorithmically, and through optimization methods.

Network Flows Meets Simplex

Explores network flows, simplex method, linear programming, tree solutions, and dual solutions in optimization problems.

Branch & Bound: Optimization

Covers the Branch & Bound algorithm for efficient exploration of feasible solutions and discusses LP relaxation, portfolio optimization, Nonlinear Programming, and various optimization problems.

Mixed-Integer Linear Programming: Formulations and Applications

Explores mixed-integer linear programming, binary variables, 0-1 knapsack, assignment problems, and LP relaxation strength.