Automorphisms and Isomorphisms of Maps in Linear Time

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43974701" target="_blank" >RIV/49777513:23520/25:43974701 - isvavai.cz</a>

Result on the web

<a href="https://dl.acm.org/doi/10.1145/3686798" target="_blank" >https://dl.acm.org/doi/10.1145/3686798</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3686798" target="_blank" >10.1145/3686798</a>

Result language

angličtina

Original language name

Automorphisms and Isomorphisms of Maps in Linear Time

Original language description

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. Every automorphism of a map determines an angle-preserving homeomorphism of the surface. While it is conjectured that there is no &quot;truly subquadratic&quot; 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 on an orientable surface of genus g not equal 0, parametrized by the genus g . A map on an orientable surface is uniform if the cyclic vector of sizes of faces incident to a vertex v does not depend on the choice of v . 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 associated uniform map in linear time. We also extend the algorithm to non-orientable surfaces by making use of the antipodal double-cover. The algorithm can be used to solve the map isomorphism problem between maps (orientable or non-orientable) of bounded negative Euler characteristic.

Czech name

—

Czech description

—

Type

J_imp - 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)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

ACM Transactions on Algorithms

ISSN

1549-6325

e-ISSN

1549-6333

Volume of the periodical

21

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

32

Pages from-to

nestránkováno

UT code for WoS article

001399998600003

EID of the result in the Scopus database

—