Oracles for Distances Avoiding a Failed Node or Link

We consider the problem of preprocessing an edge-weighted directed graph $G$ to answer queries that ask for the length and first hop of a shortest path from any given vertex $x$ to any given vertex $y$ avoiding any given vertex or edge. As a natural application, this problem models routing in networ...

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Vydáno v:SIAM journal on computing Ročník 37; číslo 5; s. 1299 - 1318
Hlavní autoři: Demetrescu, Camil, Thorup, Mikkel, Chowdhury, Rezaul Alam, Ramachandran, Vijaya
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2008
Témata:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Failure
Graph theory
Graphs
Information retrieval. Graph
Mathematics
Miscellaneous
Queries
Sciences and techniques of general use
Theoretical computing
68P05
Vertex
Query
68W01
Node
90B18
Network
data structures
Oracle
Distance
Failure
graph algorithms
Edge(graph)
Construction
network failures; 05C85
Shortest path
Algorithm
Failures
Weighted graph
shortest paths
Network routing
Digraph
Application
Directed graph
Link
05C38
ISSN:0097-5397, 1095-7111
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Popis
Shrnutí:We consider the problem of preprocessing an edge-weighted directed graph $G$ to answer queries that ask for the length and first hop of a shortest path from any given vertex $x$ to any given vertex $y$ avoiding any given 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 $G$. The construction time for our oracle is $O(mn^{2} + n^{3}\log n)$. However, if one is willing to settle for $\Theta (n^{2.5})$ space, we can improve the preprocessing time to $O(mn^{1.5}+n^{2.5}\log n)$ while maintaining the 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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539705429847