On the exponent of the all pairs shortest path problem
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
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
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Erratum to "Vickrey Pricing and Shortest Paths: What is an Edge Worth?"
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Finding the most vital node of a shortest path
Theoretical Computer Science - 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
Finding the k shortest simple paths: A new algorithm and its implementation
ACM Transactions on Algorithms (TALG)
Finding the k shortest simple paths: A new algorithm and its implementation
ACM Transactions on Algorithms (TALG)
An edge-wise linear shortest path algorithm for non negative weighted undirected graphs
Proceedings of the 7th International Conference on Frontiers of Information Technology
Fast top-k simple shortest paths discovery in graphs
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the $k$ Shortest Simple Paths Problem in Weighted Directed Graphs
SIAM Journal on Computing
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
Computing replacement paths in surface embedded graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the 13th ACM Conference on Electronic Commerce
Finding Alternative Shortest Paths in Spatial Networks
ACM Transactions on Database Systems (TODS)
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We prove superlinear 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 Ω(m &sqrt;n) time in the worst case whenever m = O(n &sqrt;n). Our construction also implies a similar lower bound on the k shortest simple 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 simple paths) can be solved in near-linear time for undirected graphs.