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

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

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

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

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

Result continuities

  • Project

    <a href="/en/project/GC19-17314J" target="_blank" >GC19-17314J: Geometric Representations of Graphs</a><br>

  • Continuities

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

Others

  • Publication year

    2021

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Algorithmica

  • ISSN

    0178-4617

  • e-ISSN

  • Volume of the periodical

    83

  • Issue of the periodical within the volume

    12

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    32

  • Pages from-to

    3649-3680

  • UT code for WoS article

    000692063300001

  • EID of the result in the Scopus database

    2-s2.0-85114101356