Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
BLASTING through the information theoretic barrier with FUSION TREES
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Computing dominances inEn (short communication)
Information Processing Letters
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
All pairs shortest paths for graphs with small integer length edges
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Buckets, Heaps, Lists, and Monotone Priority Queues
SIAM Journal on Computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Communications of the ACM
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Using Multi-level Graphs for Timetable Information in Railway Systems
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Finding a maximum weight triangle in n3-Δ time, with applications
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Efficient models for timetable information in public transportation systems
Journal of Experimental Algorithmics (JEA)
All-pairs bottleneck paths for general graphs in truly sub-cubic time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Boolean matrix multiplication and transitive closure
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
LCA queries in directed acyclic graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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A travel booking office has timetables giving arrival and departure times for all scheduled trains, including their origins and destinations. A customer presents a starting station and demands a route with perhaps several train connections taking him to his destination as early as possible. The booking office must find the best route for its customers. This problem was first considered in the theory of algorithms by Minty [1958], who reduced it to a problem on directed edge-weighted graphs: find a path from a given source to a given target such that the consecutive weights on the path are nondecreasing and the last weight on the path is minimized. Minty gave the first algorithm for the single-source version of the problem, in which one finds minimum last weight nondecreasing paths from the source to every other vertex. In this article we give the first linear-time algorithm for this problem in the word-RAM model of computation. We also define an all-pairs version for the problem and give a strongly polynomial truly subcubic algorithm for it. Finally, we discuss an extension of the problem in which one also has prices on trip segments and one wishes to find a cheapest valid itinerary.