INVENTS BEAUTIFUL THEORY OF ALGORITHMIC COMPLEXITY
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Don't Give Up
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Gavril's Approximation Algorithm
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Max-Cut
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A technicality: Optimization vs. Decision
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Today: A case study of
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GreedyVC example
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Greedyvc analysis
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A bad graph for GreedyVc
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A worse graph for GreedyVc
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Even worse graph for GreedyVc
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Greed is Bad (for Vertex-Cover)
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Gavril to the rescue
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Theorem: GavrilVC is a 2-approximation for Vertex-Cover.
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"k-Coverage" problem
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"Pokémon-Coverage" problem
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Example with k=3
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Greed is Pretty Good (for k-Coverage)
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TSP (Traveling Salesperson Problem)
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TSP example
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Textbooks
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"Popular" books
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Museum exhibits
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Movies
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Basic Approximation Algorithm: The MST Heuristic
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MST Heuristic example
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MST Heuristic Theorem: MST Heuristic is factor-2 approximation.
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Can we do better?
Description:
Explore approximation algorithms in this comprehensive lecture. Delve into the beautiful theory of algorithmic complexity and learn about various approximation techniques. Discover Gavril's Approximation Algorithm and its application to the Max-Cut problem. Examine the Greedy Vertex Cover algorithm, analyzing its performance and limitations through examples. Investigate the k-Coverage problem and its real-world applications, such as the "Pokémon-Coverage" problem. Study the Traveling Salesperson Problem (TSP) and learn about the MST Heuristic as a basic approximation algorithm. Gain insights into the theoretical foundations and practical applications of approximation algorithms in computer science and optimization.