Dual-failure distance and connectivity oracles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A nearly optimal oracle for avoiding failed vertices and edges
Proceedings of the forty-first annual ACM symposium on Theory of computing
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Connectivity oracles for failure prone graphs
Proceedings of the forty-second ACM symposium on Theory of computing
New data structures for subgraph connectivity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On the $k$ Shortest Simple Paths Problem in Weighted Directed Graphs
SIAM Journal on Computing
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
An experimental study on approximating K shortest simple paths
ESA'11 Proceedings of the 19th European conference on Algorithms
Single source distance oracle for planar digraphs avoiding a failed node or link
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The impact of edge deletions on the number of errors in networks
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Replacement paths and k simple shortest paths in unweighted directed graphs
ACM Transactions on Algorithms (TALG)
Connectivity oracles for planar graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Finding Alternative Shortest Paths in Spatial Networks
ACM Transactions on Database Systems (TODS)
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
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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.