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Spanning Trees

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Prims MST Algorithm Algorithm ( this is also greedy) Select an arbitrary vertex to start the tree, while there are fringe vertices: 1)select an edge of minimum weight between a tree vertex and a fringe vertex. 2)add the selected edge and the fringe vertex to the tree. end.

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Prims Algorithm Minimal Spanning Tree 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6 Example: start with 7

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Prims Algorithm Minimal Spanning Tree 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 2 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 2 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 6

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1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 6

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1 6 24 35 2 1 4 4 2 5 3 4 78 1 2 6

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1 6 24 35 2 1 4 4 2 5 3 4 78 1 2 6

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1 6 24 35 2 1 4 2 5 3 4 78 1 2 6

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1 6 24 35 2 1 4 2 5 3 4 78 1 2 6

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1 6 24 35 2 1 2 5 3 4 78 1 2

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1 6 24 35 2 1 2 5 3 4 78 1 2

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1 6 24 35 2 1 2 3 78 1 2 MST weight = 15 4

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Topological Sorting Algorithm while (the graph has a node with no successor) do remove one of those nodes from the graph and add it to the end of a list if (the graph is empty) then the list contains the reverse of some topological order else the graph contains a cycle

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A B C D E F G HI J L K M

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A B C D E F G HI J L K M D

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A B C E F G HI J L K M D E

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A B C F G HI J L K M DE F

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A B C G HI J L K M DEF C

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A B G HI J L K M DEFC B

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A G H I J L K M DEFCB I

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A G H J L K M DEFCBI H

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A G J L K M DEFCBIH G

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A J L K M DEFCBIHG A

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J L K M DEFCBIHGA K

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J L M DEFCBIHGAK M

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J L DEFCBIHGAKM L

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J DEFCBIHGAKML J

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DEFCBIHGAKMLJ J L M K A G H I B C F E D

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1.1 Data Structure and Algorithm Lecture 13 Minimum Spanning Trees Topics Reference: Introduction to Algorithm by Cormen Chapter 13: Minimum Spanning Trees.

1.1 Data Structure and Algorithm Lecture 13 Minimum Spanning Trees Topics Reference: Introduction to Algorithm by Cormen Chapter 13: Minimum Spanning Trees.

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