CS252 Algorithms
Monday, 8 April 2024

+ Next up
- Graphs
- Exam next Monday
    - Info about exam Wednesday

+ Questions on HW, etc.

+ Graphs: basic definitions & facts
- (Undirected) graph
    - Nodes/vertices (V, book uses n = |V|)
    - Edges (E, book uses m = |E|)
- Directed graph ("digraph")
- Degree of a node (undirected/directed?)
- Maximum |E|
- Path (undirected/directed?)
- Cycle (undirected/directed?)
- Eulerian path/cycle (visit every edge)
- Hamiltonian path/cycle (visit every vertex)
- Connected graph
- Strongly connected directed graph
- Weakly connected directed graph
- Planar graphs
- Tree
    - rooted tree: root, leaf
    - definition possibilities (there's a theorem that all 3 defs give the same objects)
        - *connected graph with no cycles
        - connected graph with n nodes and n - 1 edges
        - graph with n nodes, n - 1 edges, and no cycles

+ Implementations
- Adjacency matrix
- Adjacency lists

+ Applications
- From book
    - transportation network (nodes = airports, edges = flights)
        (directed? cuz flights go one way)
    - communication network (nodes = computer/devices, edges = some sort of
            "direct" network connection)
        (directed? [upload/download are different]; undirected? [they can both talk])
    - web pages (nodes = web pages, edges = links)
        (directed)
    - social networks (nodes = profile/account, edges = follows/friends)
        (directed? [twitter, instagram] undirected? [facebook, linkedin])
    - dependencies (nodes = tasks, edges = task A has to be done before task B)
        (directed)

- More ideas?
    - who talks to whom in harry potter, and how often?

- cells in a spreadsheet (with formula references); what does a cycle mean?
- regions on a map
    - four-color theorem
- road intersections
    - all the mapping apps
- rooms/spaces in a house
- electrical connections in a microcircuit
    - how do you print the connections without crossings?

- points in a plane (Voronoi diagrams, Delaunay triangulations)
- in the proof of the art gallery theorem
- late this term: network flows

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- From Slack
    - "Both BFS and DFS feel like very brute force algorithms, it feels like
       there should be a clever, faster solution..."
    - "In real-world comp-sci applications of graph traversal, are
        'pure' BFS or 'pure' DFS ever the best option?"


+ Algorithm categories
- Traversal
- Topological sort
- [Greedy Algorithms, starting with interval scheduling]
- Shortest paths
- Spanning trees

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