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Minimum Spanning Tree
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Minimum Spanning Tree

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Minimum Spanning Tree Minimum Spanning Tree Presentation Transcript

  • MINIMUM spANNING Trees!
    By: Makenna , Emmely , and Jessica
  • What is a minimun spanning tree?
    A graph that connects all nodes together.
    A minimum spanning tree is used to find the shortest route.
  • Basics
    Graph- a diagram showing
    MST-minimum spanning tree
    Shortest route, the shortest path between all the places you need to go
  • MST Basics
    NO CYCLES ALLOWED!
    Algorithm- a problem solving procedure following a set of rules.
    Cycle-the nodes are connected by more than one edge.
  • Muddy City
    An example would be having to use the least amount of paving stones to pave roads so that every house could be connected to every other house indirectly.
  • What is an MST Algorithm?
    An MST algorithm is a way to show the shortest distance.
    There are many different algorithms.
    Kruskal
    Prim
    Reverse delete
  • Kruskal’s Algorithm
    Pick out the smallest edges
    Repeat step 1 as long as the edge selected does not create a cycle
    When all nodes have been connected you are done
  • Kruskal #0
  • Kruskal #1
  • Kruskal #2
  • Kruskal #3
  • Kruskal #4
  • Kruskal #5
    28 stones
  • Reverse-Delete Algorithm
    This is the opposite of Kruskal’s algorithm.
    Start with all edges
    Delete the longest edge
    Continue deleting longest edge as long as all nodes are connected and no cycles.
  • Reverse-Delete #1
  • Reverse-Delete #2
  • Reverse-Delete #3
  • Reverse-Delete #4
  • Reverse-Delete #5
  • Reverse-Delete #6
  • Reverse-Delete #7
  • Reverse-Delete #8
  • Reverse-Delete #9
  • Reverse-Delete #10
  • Reverse-Delete #11
  • Prim’s Algorithm
    Pick out a node.
    Pick out the shortest edge that is connected to your tree so far as long as it doesn’t create a cycle.
    Continue this until all nodes are covered.
  • Prim #1
  • Prim #2
  • Prim #3
  • Prim #4
  • Prim #5
  • Prim #6
  • Prim #7
  • Prim #8
  • Prim #9
  • Prim #10
  • MSTs
    Kruskal (1956) and Prim (1967)
    MSTs make our life easier and we save money by using short paths.
    MST’s was first seen in Poland, France , The Czech Republic and Slovokia Czechoslovakia.
  • Importance of MSTs
    We need it in computer science because it prevents loops in a switched network with redundant paths.
    It’s one of the oldest and most basic graphs in theoretical computer science.
  • Why We Love MSTs
    MSTs are very fun to work with
    It helps you find the shortest route.
  • ANY QUESTIONS?
  • Thanksfor listening!