Automorphisms and Isomorphisms of Maps in Linear Time

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43962831" target="_blank" >RIV/49777513:23520/21:43962831 - isvavai.cz</a>

Výsledek na webu

<a href="https://drops.dagstuhl.de/opus/volltexte/2021/14068/pdf/lipics-vol198-icalp2021-complete.pdf" target="_blank" >https://drops.dagstuhl.de/opus/volltexte/2021/14068/pdf/lipics-vol198-icalp2021-complete.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2021.86" target="_blank" >10.4230/LIPIcs.ICALP.2021.86</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Automorphisms and Isomorphisms of Maps in Linear Time

Popis výsledku v původním jazyce

A map is a 2-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. An automorphism of a map can be thought of as a permutation of the vertices which preserves the vertex-edge-face incidences in the embedding. When the underlying surface is orientable, every automorphism of a map determines an angle-preserving homeomorphism of the surface. While it is conjectured that there is no “truly subquadratic” algorithm for testing map isomorphism for unconstrained genus, we present a linear-time algorithm for computing the generators of the automorphism group of a map, parametrized by the genus of the underlying surface. The algorithm applies a sequence of local reductions and produces a uniform map, while preserving the automorphism group. The automorphism group of the original map can be reconstructed from the automorphism group of the uniform map in linear time. We also extend the algorithm to non-orientable surfaces by making use of the antipodal double-cover.

Název v anglickém jazyce

Automorphisms and Isomorphisms of Maps in Linear Time

Popis výsledku anglicky

A map is a 2-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. An automorphism of a map can be thought of as a permutation of the vertices which preserves the vertex-edge-face incidences in the embedding. When the underlying surface is orientable, every automorphism of a map determines an angle-preserving homeomorphism of the surface. While it is conjectured that there is no “truly subquadratic” algorithm for testing map isomorphism for unconstrained genus, we present a linear-time algorithm for computing the generators of the automorphism group of a map, parametrized by the genus of the underlying surface. The algorithm applies a sequence of local reductions and produces a uniform map, while preserving the automorphism group. The automorphism group of the original map can be reconstructed from the automorphism group of the uniform map in linear time. We also extend the algorithm to non-orientable surfaces by making use of the antipodal double-cover.

Druh

D - Stať ve sborníku

CEP obor

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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/GA20-15576S" target="_blank" >GA20-15576S: Nakrývání grafů: Symetrie a složitost</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 statě ve sborníku

48th International Colloquium on Automata, Languages, and Programming

ISBN

978-3-95977-195-5

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

15

Strana od-do

"86:1"-"86:15"

Název nakladatele

Dagstuhl Publishing

Místo vydání

Saarbrücken/Wadern

Místo konání akce

Glasgow

Datum konání akce

12. 7. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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