On the exponent of the all pairs shortest path problem
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
The complexity of finding most vital arcs and nodes
The complexity of finding most vital arcs and nodes
SIAM Journal on Computing
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the Most Vital Node of a Shortest Path
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th 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
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Finding the anti-block vital edge of a shortest path between two nodes
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
A near-linear-time algorithm for computing replacement paths in planar directed graphs
ACM Transactions on Algorithms (TALG)
Solving the replacement paths problem for planar directed graphs in O(n log n) time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Efficiently answering probability threshold-based shortest path queries over uncertain graphs
DASFAA'10 Proceedings of the 15th international conference on Database Systems for Advanced Applications - Volume Part I
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Hierarchical phrase-based translation representations
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Improved algorithms for replacement paths problems in restricted graphs
Operations Research Letters
Replacement paths and k simple shortest paths in unweighted directed graphs
ACM Transactions on Algorithms (TALG)
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
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We prove super-linear lower bounds for some shortest path problems in directed graphs, where no such bounds were previously known. The central problem in our study is the replacement paths problem: Given a directed graph G with non-negative edge weights, and a shortest path P = {e1, e2, ..., ep} between two nodes s and t, compute the shortest path distances from s to t in each of the p graphs obtained from G by deleting one of the edges ei. We show that the replacement paths problem requires 驴(m驴n) time in the worst case whenever m = O(n驴n). Our construction also implies a similar lower bound for the k shortest paths problem for a broad class of algorithms that includes all known algorithms for the problem. To put our lower bound in perspective, we note that both these problems (replacement paths and k shortest paths) can be solved in near linear time for undirected graphs.