Decomposition of Graphs 1-Welcome
Welcome
Decomposition of Graphs 1-Graph Basics
Graph Basics
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Representing Graphs
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Slides and External References
Decomposition of Graphs 1-Exploring Undirected Graphs
Exploring Graphs
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Connectivity
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Previsit and Postvisit Orderings
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Slides and External References
Decomposition of Graphs 2-Directed Graphs
Directed Acyclic Graphs
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Topological Sort
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Strongly Connected Components
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Computing Strongly Connected Components
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Slides and External References
Paths in Graphs 1-Breadth-First Search
Applications
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Paths and Distances
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Breadth-First Search
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Breadth-First Search (continued)
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Implementation and Analysis
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BFS Properties
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Correct Distances
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Shortest Path Tree
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Slides and External References
Paths in Graphs 2-Fastest Route
Fastest Route
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Naive Algorithm
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Dijkstra's Algorithm
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Dijkstra Example
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Implementation
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Proof of Correctness
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Analysis
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Slides and External References
Paths in Graphs 2-Currency Exchange
Currency Exchange
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Reduction to Shortest Paths
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Bellman-Ford Algorithm
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Proof of Correctness
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Negative Cycles
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Infinite Arbitrage
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Slides and External References
Minimum Spanning Trees-Minimum Spanning Trees
Building a Network
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Greedy Algorithms
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Cut Property
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Kruskal's Algorithm
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Prim's Algorithm
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Slides and External References
Advanced Shortest Paths Project (Optional)-Bidirectional Dijkstra
Programming Project: Introduction
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Bidirectional Search
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Six Handshakes
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Bidirectional Dijkstra
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Finding Shortest Path after Meeting in the Middle
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Computing the Distance
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Slides and External References
Advanced Shortest Paths Project (Optional)-A-star Algorithm (A*)
A* Algorithm
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Performance of A*
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Bidirectional A*
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Potential Functions and Lower Bounds
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Landmarks (Optional)
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Slides and External References
Advanced Shortest Paths Project (Optional)-Contraction Hierarchies
Highway Hierarchies and Node Importance
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Preprocessing
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Witness Search
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Query
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Proof of Correctness
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Node Ordering
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Slides and External Refernces