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Clique-Width of Point Configurations

Result description

While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of clique-width to geometric point configurations represented by their order type. We study basic properties of this clique-width notion, and show that it is aligned with the general concept of clique-width of relational structures by Blumensath and Courcelle (2006). We also relate the new notion to monadic second-order logic of point configurations. As an application, we provide several linear FPT time algorithms for geometric point problems which are NP-hard in general, in the special case that the input point set is of bounded clique-width and the clique-width expression is also given.

Keywords

point configurationorder typefixed-parameter tractabilityrelational structureclique-width

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    Clique-Width of Point Configurations

  • Original language description

    While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of clique-width to geometric point configurations represented by their order type. We study basic properties of this clique-width notion, and show that it is aligned with the general concept of clique-width of relational structures by Blumensath and Courcelle (2006). We also relate the new notion to monadic second-order logic of point configurations. As an application, we provide several linear FPT time algorithms for geometric point problems which are NP-hard in general, in the special case that the input point set is of bounded clique-width and the clique-width expression is also given.

  • Czech name

  • Czech description

Classification

  • Type

    Jimp - 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

Others

  • Publication year

    2023

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Journal of Combinatorial Theory, Ser B

  • ISSN

    0095-8956

  • e-ISSN

  • Volume of the periodical

    158

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    31

  • Pages from-to

    43-73

  • UT code for WoS article

    000901805500003

  • EID of the result in the Scopus database

    2-s2.0-85115385971

Result type

Jimp - Article in a specialist periodical, which is included in the Web of Science database

Jimp

OECD FORD

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

Year of implementation

2023