Graph theory and software engineering it1

Transcript

1. Milda Glebauskaitė
   Graph theory and software
   engineering
   

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2. PART 1: Basics
   a.k.a stuff I should have learned in the university but I wasn’t listening
   

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3. ORIGINS
   

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4. ORIGINS
   

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5. ORIGINS
   ● There should not be any
   uncrossed bridges
   ● Each bridge must not be
   crossed more than once.
   

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6. ORIGINS
   ● There should not be any
   uncrossed bridges
   ● Each bridge must not be
   crossed more than once.
   

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7. ORIGINS
   ● 4 lands, 7 bridges
   ● There are an odd number
   of bridges connected to
   each land
   ● if you enter a land by
   crossing one bridge, you
   can always leave the land
   by crossing its second
   bridge. If third bridge
   appears, you won’t be able
   to leave a land.
   

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8. ORIGINS
   ● If new bridge appears, you
   can can solve the problem
   

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9. ORIGINS
   ● If new bridge appears, you
   can can solve the problem
   

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10. ORIGINS
    

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11. ORIGINS
    Vertex
    Edge
    

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12. ORIGINS
    Degree of a vertex, the number of edges incident connected to the
    vertex.
    

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13. ORIGINS
    An Euler path of a finite undirected graph G(V, E) is a path such that every edge of
    G appears on it once. If G has an Euler path, then it is called an Euler graph.
    

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14. ORIGINS
    Theorem. A finite undirected connected graph is an Euler graph if and only if
    exactly two vertices are of odd degree or all vertices are of even degree.
    In the latter case, every Euler path of the graph is a circuit, and in the former
    case, none is.
    

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15. Graph representation
    

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16. Graph representation
    Twitter problem
    

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17. Graph representation
    

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18. Graph representation
    

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19. Graph representation
    

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20. Graph representation
    Adjacency list - each list describes the set of neighbors of a
    vertex in the graph
    

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21. Graph representation
    

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22. Graph algorithms
    Any processing done with graphs can be called “graph algorithm”
    

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23. Graph algorithms
    Uber/Google Maps problem
    

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24. Graph algorithms
    

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25. Graph algorithms
    

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26. Dijkstra’s algorithm
    Graph algorithms
    

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27. Dijkstra’s algorithm
    1) Mark all nodes unvisited. Create a set of all the
    unvisited nodes called the unvisited set.
    2) Assign to every node a tentative distance value:
    set it to zero for our initial node and to infinity for all
    other nodes. Set the initial node as current.
    Graph algorithms
    

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28. Dijkstra’s algorithm
    1) Mark all nodes unvisited. Create a set of all the
    unvisited nodes called the unvisited set.
    2) Assign to every node a tentative distance value:
    set it to zero for our initial node and to infinity for all
    other nodes. Set the initial node as current.
    Graph algorithms
    

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29. Dijkstra’s algorithm
    3) For the current node, consider all of its unvisited
    neighbors and calculate their tentative distances
    through the current node. Compare the newly
    calculated tentative distance to the current
    assigned value and assign the smaller one.
    Graph algorithms
    

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30. Dijkstra’s algorithm
    4) When we are done considering all of the
    neighbors of the current node, mark the current
    node as visited and remove it from the unvisited
    set. A visited node will never be checked again.
    Graph algorithms
    

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31. Dijkstra’s algorithm
    5) If the destination node has been marked visited
    (when planning a route between two specific
    nodes) or if the smallest tentative distance among
    the nodes in the unvisited set is infinity (when
    planning a complete traversal; occurs when there
    is no connection between the initial node and
    remaining unvisited nodes), then stop. The
    algorithm has finished.
    6) Otherwise, select the unvisited node that is
    marked with the smallest tentative distance, set it
    as the new “current node”, and go back to step 3.
    Graph algorithms
    

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32. Dijkstra’s algorithm
    5) If the destination node has been marked visited
    (when planning a route between two specific
    nodes) or if the smallest tentative distance among
    the nodes in the unvisited set is infinity (when
    planning a complete traversal; occurs when there
    is no connection between the initial node and
    remaining unvisited nodes), then stop. The
    algorithm has finished.
    6) Otherwise, select the unvisited node that is
    marked with the smallest tentative distance, set it
    as the new “current node”, and go back to step 3.
    Graph algorithms
    

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33. PART 2: Graphs are fun
    a.k.a stuff I found interesting but did not know how to structure into proper
    presentation
    

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34. GT in Model based testing
    Model based testing is a software testing technique where run time behavior of software under test is checked
    against predictions made by a model. A model is a description of a system's behavior.
    

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35. MBT
    ▪ You create model of a SUT
    ▪ It’s a simplified model
    ▪ It’s a state model defining states and
    relationships between them
    ▪ From this model you can generate tests
    and execute them on SUT
    

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36. GT in MBT
    ▪ Chinese postman problem solutions
    ▪ de Bruijn sequences algorithm
    ▪ Random Walk algorithm
    

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37. Graph coloring problem
    Given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored
    using same color.
    

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38. Real life problems
    ▪ Schedules and timetables
    ▪ Map coloring
    ▪ Sudoku
    

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39. More fancy problems
    ▪ Register allocation
    

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40. In compiler optimization, register allocation is the process of assigning a
    large number of target program variables onto a small number of CPU
    registers.
    

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41. Nodes in the graph represent live ranges (variables, temporaries,
    virtual/symbolic registers) that are candidates for register allocation. Edges
    connect live ranges that interfere , i.e., live ranges that are simultaneously
    live at at least one program point. Register allocation then reduces to the
    graph coloring problem in which colors (registers) are assigned to the nodes
    such that two nodes connected by an edge do not receive the same color.
    

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42. More fancy problems
    ▪ Register allocation
    ▪ Network updates
    

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43. OO programs as graphs
    

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44. GT in OO programs
    ▪ Identification of “God” classes
    - HyperLink Induced Topic Search algorithm
    

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45. Hyperlink-Induced Topic Search is a link analysis algorithm that rates Web
    pages. The scheme assigns two scores for each page: its authority, which
    estimates the value of the content of the page, and its hub value, which
    estimates the value of its links to other pages.
    

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46. GT in OO programs
    ▪ Identification of “God” classes
    - HyperLink Induced Topic Search algorithm
    ▪ Design pattern detection
    - graph matching algorithms
    

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47. Thank You
    

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48. P.S. I stole the illustrations from this post
    ▪ https://www.freecodecamp.org/news/i-dont-understan
    d-graph-theory-1c96572a1401/
    

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