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Lecture
Approximation Algorithms
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Related lectures (38)
Set Cover: Integrality Gap
Explores the integrality gap concept in set cover and multiplicative weights algorithms.
Optimization Methods: Theory Discussion
Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.
Linear Programming: Weighted Bipartite Matching
Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.
Cartesian Product and Induction
Introduces Cartesian product and induction for proofs using integers and sets.
Optimisation in Energy Systems
Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.
Algorithms & Growth of Functions
Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.
Minimum Spanning Trees: Prim's Algorithm
Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.
Complex Systems: Critical Phenomena
Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.
Unweighted Bipartite Matching
Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.
Mapping Functions and Surjections
Explores mapping functions, surjections, injective and surjective functions, and bijective functions.
Graphical Models: Representing Probabilistic Distributions
Covers graphical models for probabilistic distributions using graphs, nodes, and edges.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Linear Programming Duality
Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.
Composition of Applications in Mathematics
Explores the composition of applications in mathematics and the importance of understanding their properties.
Matroids: Matroid Intersection
Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.
Graph Sketching: Connected Components
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Covers the concept of graph sketching with a focus on connected components.
Semi-Definite Programming
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Covers semi-definite programming and optimization over positive semidefinite cones.
Integer Optimization: Theory and Applications
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Covers the fundamentals of integer optimization, including integer programming, dynamic programming, and approximation algorithms.
Sparsest Cut: ARV Theorem
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Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.
Constrained optimization: the basics
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Covers the basics of constrained optimization, including tangent directions, trust-region subproblems, and necessary optimality conditions.
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