Long paths in hypercubes with a quadratic number of faults

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00206366" target="_blank" >RIV/00216208:11320/09:00206366 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Long paths in hypercubes with a quadratic number of faults
Original language description
A path between distinct vertices u and v of the n-dimensional hypercube Q(n) avoiding a given set of f faulty vertices is called long if its length is at least 2^n-2f-2. We present a function phi(n) = Theta(n^2) such that if f {= phi(n) then there is a long fault-free path between every pair of distinct vertices of the largest fault-free block of Q(n). Moreover, the bound provided by phi(n) is asymptotically optimal. Furthermore, we show that assuming f {= phi(n), the existence of a long fault-free pathbetween an arbitrary pair of vertices may be verified in polynomial time with respect to n and, if the path exists, its construction performed in linear time with respect to its length.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)