Mathieu Chapelle1 Frederic Mazoit2 Ioan Todinca1

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Mathieu Chapelle , Frédéric Mazoit , Ioan Todinca

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Constructing brambles Mathieu Chapelle1, Frederic Mazoit2, Ioan Todinca1 1LIFO – Universite d'Orleans 2LaBRI – Universite de Bordeaux I JGA'09 Montpellier 5–6 novembre 2009

tree-like decompositions

when restricted

brambles revisited

tree width

width

constructing brambles

used when

Voir

Publié par

pefav

Langue

English

Tree decomposition

Mathieu

Constructing brambles

Chapelle1Fr,d´´eicerozaMti2, Ioan

1LIFiverO–UndeO’is´tnaslre´ 2UnI–BRLat´sierivedroBedeIxua

JGA’09 Montpellier 5–6 novembre 2009

Todinca1

hTdeglaetirooCmhradblembevsritisceitevsnclusionandpersp

The algorithm

Conclusion and perspectives

Tree-decompositions and brambles revisited

The problem

1/2-eerTmelborpehT0annsioitosmpcode

Tree-decompositions and brambles revisited

The problem

Conclusion and perspectives

The algorithm

compositmTree-deehrpboel22/T0orlgeaTheditisevrselbmarbdnasnoistivespecdpernonaulisoCcntimh

lemsprobhardlNP-pnloevidseloacbnrteainrlloiaomynetcirtsernehwemih,andglupapproactuoisnotsebus-lobaloollstaobaginfostausuoituoL.ntdgoarhpwstibhuonded∗-widths.

3/20

Tree-like decompositions

A popular technique used when dealing withN P-hard problems is todecomposethe input graph and then usedynamic programming.

heTborpTmel-eerocedulcnoCmhtiroglaetiecsperdpanonsibdarsnnatioipmsoedThisitsrevmbleevseuw-diht.,..lAwl,rank-width,cliq,htdnarbw-hchtdig.e.re:twie-sinapartesubdglu,hnargpatyehvilerscuresepoomec•d:rovaﬂemasniskrobottom-u;•applyaopisitnoihdscemovegiytnbid-wisth•;ee∗ehtdnikrtfo

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A popular technique used when dealing withN P-hard problems is todecomposethe input graph and then usedynamic programming. e.g.:tree-width, branch-width, rank-width, clique-width, . . .

Tree-like decompositions

laroilenraitemhwenrestrictedtogrlborpdraebnacsmeinedlvsominolypobolaanlgitnoosulsofu.LotNP-hsual

alsufusootL-hNPdparblroscemebnavlosnideylopnomialorlineartiemhwneertsirtcdehsapgrtounbothwidiw-∗ded

All works in same ﬂavor: •decompose recursivelythe graph, and glue subparts in a kind of tree; •the∗-width is given by this decomposition; •apply abottom-upapproach, and glue sub-solutions to obtain a global solution.

A popular technique used when dealing withN P-hard problems is todecomposethe input graph and then usedynamic programming. e.g.:tree-width . ., branch-width, rank-width, clique-width, .

Tree-like decompositions

.shtsreptcvioiandnepmConclusalgorithetisehTdselbiverndsaambrsipoonticemoeed-merTorlbThep3/20se

3/2-eerTmelborpehT0annsioitosmpcodesitirsvebmelbdarhmCooritealgedThevsceitsionncluerspandp

Tree-like decompositions

A popular technique used when dealing withN P-hard problems is todecomposethe input graph and then usedynamic programming. e.g.:tree-width, branch-width, rank-width, clique-width, . . .

Lots of usualN P-hard problems can be solved in polynomial or linear time when restricted to graphs with bounded∗-widths.

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