Simplified Algorithmic Metatheorems Beyond MSO: Treewidth and Neighborhood Diversity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403798" target="_blank" >RIV/00216208:11320/19:10403798 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21240/19:00337768

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-RewmvxQsc" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-RewmvxQsc</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.23638/LMCS-15(4:12)2019" target="_blank" >10.23638/LMCS-15(4:12)2019</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Simplified Algorithmic Metatheorems Beyond MSO: Treewidth and Neighborhood Diversity

Popis výsledku v původním jazyce

This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical theorem of Courcelle states that any graph property definable in MSO is decidable in linear time on graphs of bounded treewidth. Algorithmic metatheorems like Courcelle&apos;s serve to generalize known positive results on various graph classes. We explore and extend three previously studied MSO extensions: global and local cardinality constraints (CardMSO and MSO-LCC) and optimizing the fair objective function (fairMSO). First, we show how these extensions of MSO relate to each other in their expressive power. Furthermore, we highlight a certain &quot;linearity&quot; of some of the newly introduced extensions which turns out to play an important role. Second, we provide parameterized algorithm for the aforementioned structural parameters. On the side of neighborhood diversity, we show that combining the linear variants of local and global cardinality constraints is possible while keeping the linear (FPT) runtime but removing linearity of either makes this impossible. Moreover, we provide a polynomial time (XP) algorithm for the most powerful of studied extensions, i.e. the combination of global and local constraints. Furthermore, we show a polynomial time (XP) algorithm on graphs of bounded treewidth for the same extension. In addition, we propose a general procedure of deriving XP algorithms on graphs on bounded treewidth via formulation as Constraint Satisfaction Problems (CSP). This shows an alternate approach as compared to standard dynamic programming formulations.

Název v anglickém jazyce

Simplified Algorithmic Metatheorems Beyond MSO: Treewidth and Neighborhood Diversity

Popis výsledku anglicky

This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical theorem of Courcelle states that any graph property definable in MSO is decidable in linear time on graphs of bounded treewidth. Algorithmic metatheorems like Courcelle&apos;s serve to generalize known positive results on various graph classes. We explore and extend three previously studied MSO extensions: global and local cardinality constraints (CardMSO and MSO-LCC) and optimizing the fair objective function (fairMSO). First, we show how these extensions of MSO relate to each other in their expressive power. Furthermore, we highlight a certain &quot;linearity&quot; of some of the newly introduced extensions which turns out to play an important role. Second, we provide parameterized algorithm for the aforementioned structural parameters. On the side of neighborhood diversity, we show that combining the linear variants of local and global cardinality constraints is possible while keeping the linear (FPT) runtime but removing linearity of either makes this impossible. Moreover, we provide a polynomial time (XP) algorithm for the most powerful of studied extensions, i.e. the combination of global and local constraints. Furthermore, we show a polynomial time (XP) algorithm on graphs of bounded treewidth for the same extension. In addition, we propose a general procedure of deriving XP algorithms on graphs on bounded treewidth via formulation as Constraint Satisfaction Problems (CSP). This shows an alternate approach as compared to standard dynamic programming formulations.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

32

Strana od-do

1-32

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85078906302