We consider the problem of preprocessing an edge-weighted directed graph G to answer queries that ask for the length of a shortest path from any given vertex x to another given vertex y avoiding an arbitrary vertex or edge. As a natural application, this problem models routing in networks subject to node or link failures. We describe a deterministic oracle with constant query time for this problem that uses O(n^2 log n) space, where n is the number of vertices in G. We also show that if we are willing to use Theta(n^2.5) space, we can reduce the preprocessing time by a factor of n^0.5 while maintaining constant query time. Our algorithms can find the shortest path avoiding a failed node or link in time proportional to the length of the path.
Oracles for distances avoiding a failed node or link / Demetrescu, Camil; Mikkel, Thorup; Rezaul Alam, Chowdhury; Vijaya, Ramachandran. - In: SIAM JOURNAL ON COMPUTING. - ISSN 0097-5397. - 37:5(2007), pp. 1299-1318. [10.1137/S0097539705429847]
Oracles for distances avoiding a failed node or link
DEMETRESCU, Camil;
2007
Abstract
We consider the problem of preprocessing an edge-weighted directed graph G to answer queries that ask for the length of a shortest path from any given vertex x to another given vertex y avoiding an arbitrary vertex or edge. As a natural application, this problem models routing in networks subject to node or link failures. We describe a deterministic oracle with constant query time for this problem that uses O(n^2 log n) space, where n is the number of vertices in G. We also show that if we are willing to use Theta(n^2.5) space, we can reduce the preprocessing time by a factor of n^0.5 while maintaining constant query time. Our algorithms can find the shortest path avoiding a failed node or link in time proportional to the length of the path.File | Dimensione | Formato | |
---|---|---|---|
VE_2007_11573-129783.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
306.81 kB
Formato
Adobe PDF
|
306.81 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.