End of Term Review 2.6

End of Term Review 2.6 - DAGs and Topological Ordering A...

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Unformatted text preview: DAGs and Topological Ordering A directed acyclic graph (DAG) is a digraph that has no directed cycles A topological ordering of a digraph is a numbering D v1 , …, vn B of the vertices such that for every edge (vi , vj), we have i < j C DAG G A Example: in a task scheduling digraph, a topological ordering is a task sequence that satisfies the precedence constraints v4 D v2 Theorem B A digraph admits a topological ordering if and only if it is a DAG A - 76 - v5 E v3 C v1 CSE 2011 Prof. J. Elder E Topological ordering of G Last Updated: 4/1/10 2:37 PM Linear Order Alg: DFS a h i j k b c d e g f CSE 2011 Prof. J. Elder Found Not Handled Stack f g e d l - 77 - ….. f Last Updated: 4/1/10 2:37 PM Linear Order Alg: DFS a h i j k b c d e g f Found Not Handled Stack l g e d l When node is popped off stack, insert at front of linearly-ordered “to do” list. Linear Order: CSE 2011 Prof. J. Elder - 78 - ….. f Last Updated: 4/1/10 2:37 PM Linear Order Found Not Handled Stack Alg: DFS a h i j k b c d e g f g e d l Linear Order: CSE 2011 Prof. J. Elder - 79 - l,f Last Updated: 4/1/10 2:37 PM BFS Example A undiscovered A discovered (on Queue) A finished unexplored edge A L1 B discovery edge C E D F cross edge L0 L1 L0 A B C E CSE 2011 Prof. J. Elder L1 D F A B C E - 80 - D F Last Updated: 4/1/10 2:37 PM ...
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This note was uploaded on 02/14/2012 for the course CSE 2011Z taught by Professor Elder during the Fall '11 term at York University.

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End of Term Review 2.6 - DAGs and Topological Ordering A...

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