Parametrized topological complexity of poset-stratified spaces

In this paper, parametrized motion planning algorithms for a fiberwise space [Formula: see text] over a poset P are studied. Such an algorithm assigns paths in a space X decomposed into subspaces with the index set P, that do not cross the boundaries of the separated regions. We compute the parametr...

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Autor principal: Tanaka, Kohei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8683837/
https://www.ncbi.nlm.nih.gov/pubmed/34957331
http://dx.doi.org/10.1007/s41468-021-00085-z
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author Tanaka, Kohei
author_facet Tanaka, Kohei
author_sort Tanaka, Kohei
collection PubMed
description In this paper, parametrized motion planning algorithms for a fiberwise space [Formula: see text] over a poset P are studied. Such an algorithm assigns paths in a space X decomposed into subspaces with the index set P, that do not cross the boundaries of the separated regions. We compute the parametrized topological complexity of [Formula: see text] , which is one less than the minimal number of local parametrized motion planning algorithms used for designing non-cross-border robot motions in X.
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spelling pubmed-86838372021-12-20 Parametrized topological complexity of poset-stratified spaces Tanaka, Kohei J Appl Comput Topol Article In this paper, parametrized motion planning algorithms for a fiberwise space [Formula: see text] over a poset P are studied. Such an algorithm assigns paths in a space X decomposed into subspaces with the index set P, that do not cross the boundaries of the separated regions. We compute the parametrized topological complexity of [Formula: see text] , which is one less than the minimal number of local parametrized motion planning algorithms used for designing non-cross-border robot motions in X. Springer International Publishing 2021-12-18 2022 /pmc/articles/PMC8683837/ /pubmed/34957331 http://dx.doi.org/10.1007/s41468-021-00085-z Text en © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Tanaka, Kohei
Parametrized topological complexity of poset-stratified spaces
title Parametrized topological complexity of poset-stratified spaces
title_full Parametrized topological complexity of poset-stratified spaces
title_fullStr Parametrized topological complexity of poset-stratified spaces
title_full_unstemmed Parametrized topological complexity of poset-stratified spaces
title_short Parametrized topological complexity of poset-stratified spaces
title_sort parametrized topological complexity of poset-stratified spaces
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8683837/
https://www.ncbi.nlm.nih.gov/pubmed/34957331
http://dx.doi.org/10.1007/s41468-021-00085-z
work_keys_str_mv AT tanakakohei parametrizedtopologicalcomplexityofposetstratifiedspaces

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