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Introduction A polynomial instance

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Introduction A polynomial instance Reduction to the polynomial instance Conclusion Multicut is FPT Nicolas Bousquet Joint work with: Jean Daligault, Stephan Thomasse Nicolas Bousquet Multicut is FPT

  • attachment vertices

  • parameterized complexity

  • instance

  • binary tree

  • introduction parameterized complexity

  • fixed parameter

  • can branch

  • vertex

  • cover


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Language English
IntroductionApoylonimlanitsnaecduReioctotntpoheonyllaimtsniecnalusiConconasBousquNicolsituTPFuMtecitl
work
Joint
Thomass´e
with:JeanDaligault,Ste´phan
Multicut is FPT
Nicolas Bousquet
cutiulti
Introduction Parameterized complexity Multicut
1
2
sFPT
3
A polynomial instance
Reduction to the polynomial instance Vertex Multicut Reductions for one attachment vertex Two attachment vertices components
IpolyionAductntroeRecnatsnilaimonlypoheotntioctduulcnnoisaraPetemminoinalanstCoceluituctrizedcomplexityMuetMousqlasBNicoisnocnul4oC
ucedontithtoolepmonyilaiatsnCecnIntroductionApolnymoaiilsnatcnRetucitluMmatePnrasuoinolcxitympleedcoerizlosaNciuqteoBsultMuuticFPis
FPT A parameterized problem isFPT(Fixed Parameter Tractable) iff there is an algorithm which runs in timePoly(n)f(k) for an instance of sizenand of parameterk.
T
oryaxy:xedgeckanCxvoreethtVeerniranbcaweceen.HerhcihwedicedothcnoorPiP:ftttocaneooesehhctex.nverrytrBinatpedfoeesomta:khncrakbt2coNis.henoiessleceetidtnheVertexCover.Deaercbkesenoyddnaetelheetgeeddjsa
Theorem Vertex Cover parameterized by the
Example
Parameterized complexity Multicut
FPT.
is
size of the solution
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RecnatsnilaimonyolApontiucodtrIncnCesnataiilnymoepoltothtioneducizercoedlemptyxilcnooisuraPntemauMtlcituitucitFsTP
Example
Proof : Pick an edgexy:xoryare in the Vertex Cover. Hence we can branch to decide which one is selected in the Vertex Cover. Decreasekby one and delete the edges adjacent to the choosen vertex.
Theorem Vertex Cover parameterized by the size of the solution is FPT.
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T
Example
Theorem Vertex Cover parameterized by the size of the solution is FPT.
Proof : Pick an edgexy:xoryare in the Vertex Cover. Hence we can branch to decide which one is selected in the Vertex Cover. Decreasekby one and delete the edges adjacent to the choosen vertex. Binary tree of depthk: at most 2kbranches.
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