Graph_theory_Part1_students_2Pp

# Graph_theory_Part1_students_2Pp - 1 2/2/2006,rev. 9/24/06...

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Unformatted text preview: 1 2/2/2006,rev. 9/24/06 M. A. Breuer and others 1 Graphs and Related Theory and Algorithms with applications to VLSI layout Part 1 of 3 Fill-in Answer Animation Only Melvin A. Breuer EE 581 Fall 2006 University of Southern California 2/2/2006,rev. 9/24/06 M. A. Breuer and others 2 What you should get from this material on Graphs How many CAD problems can be modeled as a graph That graph theory is a well researched area with many important results Information about graphs (general and special), graph related algorithms and their complexity That CAD problems can be solved via graph algorithms That you need not re-invent the wheel 2 2/2/2006,rev. 9/24/06 M. A. Breuer and others 3 Outline Graph theory Graphs Directed, Triangular, Weighted, Complete, Complement, Sub-graphs, Embeddings Traversing graphs A Walk, Tour, Path Properties Maximum clique size, Transitive Orientations, Color, Chords, Cut-edge,In and Out-degree, Connected, etc. Types of graphs Bipartite, Comparability, Perfect, Planar, Chordal, Co- comparability, Circle, Trees, Complete, Maximal sub-graphs, Dual, Complement, Interval, Overlap, Containment, etc. 2/2/2006,rev. 9/24/06 M. A. Breuer and others 4 Outline (cont) Graph related to VLSI layout Interval, Permutation,Chordal, Co-comparability, Intersection, Containment, Neighborhood, Rectangular duals Graph problems and algorithms related to VLSI Minimal spanning tree, Minimal Steiner tree, Matching, Min- cut and Max-flow,Maximum independent set, Maximal clique, Minimal color (chromatic number), Partitioning, Network flow 2 2/2/2006,rev. 9/24/06 M. A. Breuer and others 3 Outline Graph theory Graphs Directed, Triangular, Weighted, Complete, Complement, Sub-graphs, Embeddings Traversing graphs A Walk, Tour, Path Properties Maximum clique size, Transitive Orientations, Color, Chords, Cut-edge,In and Out-degree, Connected, etc. Types of graphs Bipartite, Comparability, Perfect, Planar, Chordal, Co- comparability, Circle, Trees, Complete, Maximal sub-graphs, Dual, Complement, Interval, Overlap, Containment, etc. 2/2/2006,rev. 9/24/06 M. A. Breuer and others 4 Outline (cont) Graph related to VLSI layout Interval, Permutation,Chordal, Co-comparability, Intersection, Containment, Neighborhood, Rectangular duals Graph problems and algorithms related to VLSI Minimal spanning tree, Minimal Steiner tree, Matching, Min- cut and Max-flow,Maximum independent set, Maximal clique, Minimal color (chromatic number), Partitioning, Network flow 3 2/2/2006,rev. 9/24/06 M. A. Breuer and others 5 Motivation CAD problem Graph model Graph algorithm Graph solution CAD solution Logic circuit A corresponding graph Find critical path Test for feedback Partition circuit Etc....
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Graph_theory_Part1_students_2Pp - 1 2/2/2006,rev. 9/24/06...

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