U-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438412" target="_blank" >RIV/00216208:11320/21:10438412 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8LND2Rfgx1" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8LND2Rfgx1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-021-00837-4" target="_blank" >10.1007/s00453-021-00837-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

U-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

Popis výsledku v původním jazyce

Interval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs-a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a richer class of graphs. In particular, mixed unit interval graphs may contain a claw as an induced subgraph, as opposed to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs and demonstrate the advantages of this generalized model by providing a subexponential-time algorithm for solving the MaxCut problem on mixed unit interval graphs. In addition, we derive a polynomial-time algorithm for certain subclasses of mixed unit interval graphs. We point out a substantial mistake in the proof of the polynomiality of the MaxCut problem on unit interval graphs by Boyacı et al. (Inf Process Lett 121:29-33, 2017. https://doi.org/10.1016/j.ipl.2017.01.007). Hence, the time complexity of this problem on unit interval graphs remains open. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs.

Název v anglickém jazyce

U-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

Popis výsledku anglicky

Interval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs-a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a richer class of graphs. In particular, mixed unit interval graphs may contain a claw as an induced subgraph, as opposed to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs and demonstrate the advantages of this generalized model by providing a subexponential-time algorithm for solving the MaxCut problem on mixed unit interval graphs. In addition, we derive a polynomial-time algorithm for certain subclasses of mixed unit interval graphs. We point out a substantial mistake in the proof of the polynomiality of the MaxCut problem on unit interval graphs by Boyacı et al. (Inf Process Lett 121:29-33, 2017. https://doi.org/10.1016/j.ipl.2017.01.007). Hence, the time complexity of this problem on unit interval graphs remains open. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GC19-17314J" target="_blank" >GC19-17314J: Geometrické reprezentace grafů</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Algorithmica

ISSN

0178-4617

e-ISSN

—

Svazek periodika

83

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

3649-3680

Kód UT WoS článku

000692063300001

EID výsledku v databázi Scopus

2-s2.0-85114101356