Dynamic programming for graphs on surfaces

Ignasi Saucnrs, Lirmm, Montpellier

Description

Niveau: Supérieur
Dynamic programming for graphs on surfaces Ignasi Sau CNRS, LIRMM, Montpellier Joint work with: Juanjo Rue Ecole Polytechnique, Paris, France Instituto de Ciencias Matematicas, Madrid, Spain Dimitrios M. Thilikos Department of Mathematics, NKU of Athens, Greece [An extended abstract appeared in ICALP'10] Ignasi Sau (CNRS, LIRMM) CIRM, Marseille October 19, 2010 1 / 29

• over all


• orientable surface


• instituto de ciencias matematicas


• any compact


• joint work

Sujets

• École polytechnique
• Orientability

Informations

• Publié par: chaeh
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

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[An extended abstract appeared inICALP’10]

Dynamic programming for graphs on surfaces

Joint work with:

Ignasi Sau CNRS, LIRMM, Montpellier

Dimitrios M. Thilikos Department of Mathematics, NKU of Athens, Greece

Juanjo Rue´ ´ Ecole Polytechnique, Paris, France InstitutodeCienciasMatem ´ aticas,Madrid,Spain

9

19erobct/20201,2

2

Background

1

5

Conclusions and further research

Outline

9

Sketch of the enumerative part

4

Main ideas of our approach

3

Motivation and previous work

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Main ideas of our approach

4

Sketch of the enumerative part

Background

2

Motivation and previous work

3

30102,91

1

5

Conclusions and further research

Outline

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Tis a tree where all the internal nodes have degree 3. µis a bijection between the leaves ofTandE(G).

Abranch decompositionof a graphG= (V,E)is tuple(T, µ) where:

For eache∈E(T), we definemid(e)=V(A e )∩V(B e ).

Each edgee∈TpartitionsE(G)into two setsA e andB e .

Thebranchwidthof a graphG(denotedbw(G)) is the minimum width over all branch decompositions ofG:

Thewidthof a branch decomposition is max e∈E(T) |mid(e)|.

bw(G) = (T m , i µ n ) e∈ m E a (T x ) |mid(e)|

104/29

Branch decompositions and branchwidth

ber19,20

Orientable surfaces: obtained by addingg≥0handlesto the sphereS 2 , obtaining the g-torusT g withEuler genuseg(T g ) =2g.

Non-orientable surfaces: obtained by addingh>0cross-capsto the sphereS 2 , obtaining a non-orientable surfaceP h withEuler genuseg(P h ) =h.

Surface Classification Theorem:

any compact, connected and without boundary surface can be obtained from the sphereS 2 by addinghandlesandcross-caps.

S URFACE = TOPOLOGICAL SPACE , LOCALLY “ FLAT ”

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Surfaces

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Orientable surfaces: obtained by addingg≥0handlesto the sphereS 2 , obtaining the g-torusT g withEuler genuseg(T g ) =2g.

any compact, connected and without boundary surface can be obtained from the sphereS 2 by addinghandlesandcross-caps.

Surface Classification Theorem:

S URFACE = TOPOLOGICAL SPACE , LOCALLY “ FLAT ”

9

Surfaces

Non-orientable surfaces: obtained by addingh>0cross-capsto the sphereS 2 , obtaining a non-orientable surfaceP h withEuler genuseg(P h ) =h.

MaM,IR)CeOlleirs91rebotc2/50102,