Graph Searches Revisited A lego of graph searches
89 Pages
English
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Graph Searches Revisited A lego of graph searches

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89 Pages
English

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Niveau: Supérieur
Graph Searches Revisited : A lego of graph searches Graph Searches Revisited : A lego of graph searches Michel Habib Pretty Structures 2011, IHP, may 2011

  • tie-break rules

  • comparability graphs

  • basic graph

  • characterization using

  • graph searches

  • schedule generic

  • lexicographic depth


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Reads 10
Language English

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Graph Searches Revisited : A lego of graph searches
Graph Searches Revisited : A lego of graph searches
Michel Habib habib@liafa.jussieu.fr http://www.liafa.jussieu.fr/~habib
Pretty Structures 2011, IHP, may 2011
Graph Searches Revisited :
A lego of graph searches
Schedule Generic Search
Breadth First Search Depth First Search Lexicographic Breadth First Search LexBFS Lexicographic Depth First Search LexDFS
Maximal Neighbourhood Search (MNS) Lego with basic graph searches Importance of 4 points conditions for graph recognition The set of all simplicial schemes Principle of a Composition of Searches Hamiltonicity on co-comparability graphs
Graph Searches Revisited :
A lego of graph searches
Graph searches are very well known and used
1.
2.
3.
Euler (1735) for solving the famous walk problem in Kœnisberg Tremeaux (1882) and Tarry (1895) using DFS to solve maze problems Computer scientists from 1950 ....
Graph Searches Revisited :
A lego of graph searches
Two main aspects for a
1.
2.
graph search :
its principle or its algorithm (i.e. the description of the tie-break rules for the choice of the next vertex (edge) to be explored ) its implementation or its program
Graph Searches Revisited :
A lego of graph searches
We will focus here on a third one : Iits characterization using forbidden structures and the relationships with the algorithm Itry to convince you that these characterizations can beI will helpful
Graph Searches Revisited :
A lego of graph searches
Problem For an undirected graphG= (V,E), explore the vertices ofG”traversing or following” the edges.
Result Ia tree structure rooted at the first visited vertex Ian orderingσof the vertices
Questions IUnder which conditions an orderingσof the vertices corresponds to a search ? I ?What are the properties of these orderings
Graph Searches Revisited :
A lego of graph searches
Main reference for this today lecture :
These easy questions have been only recently systematically considered : D.G. Corneil et R. M. Krueger, A unified view of graph searching, SIAM J. Discrete Math, 22, N˚4 (2008) 1259-1276
Graph Searches Revisited : Generic Search
A lego of graph searches
Generic Search
Breadth First Search
Depth First Search
Lexicographic Breadth First Search LexBFS
Lexicographic Depth First Search LexDFS
Maximal Neighbourhood Search (MNS)
Lego with basic graph searches
Importance of 4 points conditions for graph recognition
The set of all simplicial schemes
Principle of a Composition of Searches
Hamiltonicity on co-comparability graphs