On the central levels problem
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10418932" target="_blank" >RIV/00216208:11320/20:10418932 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.4230/LIPIcs.ICALP.2020.60" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2020.60</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2020.60" target="_blank" >10.4230/LIPIcs.ICALP.2020.60</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On the central levels problem
Popis výsledku v původním jazyce
The central levels problem asserts that the subgraph of the (2m+1)-dimensional hypercube induced by all bitstrings with at least m+1-???? many 1s and at most m+???? many 1s, i.e., the vertices in the middle 2???? levels, has a Hamilton cycle for any m >= 1 and 1 <= ???? <= m+1. This problem was raised independently by Savage, by Gregor and Škrekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case ???? = 1, and classical binary Gray codes, namely the case ???? = m+1. In this paper we present a general constructive solution of the central levels problem. Our results also imply the existence of optimal cycles through any sequence of ???? consecutive levels in the n-dimensional hypercube for any n >= 1 and 1 <= ???? <= n+1. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the n-dimensional hypercube, n>= 2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code.
Název v anglickém jazyce
On the central levels problem
Popis výsledku anglicky
The central levels problem asserts that the subgraph of the (2m+1)-dimensional hypercube induced by all bitstrings with at least m+1-???? many 1s and at most m+???? many 1s, i.e., the vertices in the middle 2???? levels, has a Hamilton cycle for any m >= 1 and 1 <= ???? <= m+1. This problem was raised independently by Savage, by Gregor and Škrekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case ???? = 1, and classical binary Gray codes, namely the case ???? = m+1. In this paper we present a general constructive solution of the central levels problem. Our results also imply the existence of optimal cycles through any sequence of ???? consecutive levels in the n-dimensional hypercube for any n >= 1 and 1 <= ???? <= n+1. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the n-dimensional hypercube, n>= 2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
<a href="/cs/project/GA19-08554S" target="_blank" >GA19-08554S: Struktury a algoritmy ve velmi symetrických grafech</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-138-2
ISSN
1868-8969
e-ISSN
—
Počet stran výsledku
17
Strana od-do
1-17
Název nakladatele
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH
Místo vydání
Dagstuhl, Germany
Místo konání akce
Saarbrücken, Germany
Datum konání akce
8. 7. 2020
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
—