Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Recursive star-tree parallel data structure
SIAM Journal on Computing
Improved Distance Oracles for Avoiding Link-Failure
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
On the Difficulty of Some Shortest Path Problems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Improved distance sensitivity oracles via random sampling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Oracles for Distances Avoiding a Failed Node or Link
SIAM Journal on Computing
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Forbidden-set distance labels for graphs of bounded doubling dimension
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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 present an improved oracle for the distance sensitivity problem. The goal is to preprocess a directed graph G = (V,E) with non-negative edge weights to answer queries of the form: what is the length of the shortest path from x to y that does not go through some failed vertex or edge f. The previous best algorithm produces an oracle of size ~O(n2) that has an O(1) query time, and an ~O(n2√m) construction time. It was a randomized Monte Carlo algorithm that worked with high probability. Our oracle also has a constant query time and an ~O(n2) space requirement, but it has an improved construction time of ~O(mn), and it is deterministic. Note that O(1) query, O(n2) space, and O(mn) construction time is also the best known bound (up to logarithmic factors) for the simpler problem of finding all pairs shortest paths in a weighted, directed graph. Thus, barring improved solutions to the all pairs shortest path problem, our oracle is optimal up to logarithmic factors.