Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Faster algorithms for the shortest path problem
Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
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
Recent results on the single-source shortest paths problem
ACM SIGACT News
Buckets, Heaps, Lists, and Monotone Priority Queues
SIAM Journal on Computing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Faster deterministic sorting and priority queues in linear space
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Sorting and Searching on the Word RAM
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
A scaling algorithm for weighted matching on general graphs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
A Faster All-Pairs Shortest Path Algorithm for Real-Weighted Sparse Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Shortest Path Algorithms: Engineering Aspects
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
On the Comparison-Addition Complexity of All-Pairs Shortest Paths
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Experimental Evaluation of a New Shortest Path Algorithm
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
A Simple Shortest Path Algorithm with Linear Average Time
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A Faster Shortest-Paths Algorithm for Minor-Closed Graph Classes
Graph-Theoretic Concepts in Computer Science
Nondecreasing paths in a weighted graph or: How to optimally read a train schedule
ACM Transactions on Algorithms (TALG)
Networks cannot compute their diameter in sublinear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A faster polynomial algorithm for the constrained maximum flow problem
Computers and Operations Research
Research paper: The saga of minimum spanning trees
Computer Science Review
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
Well supported approximate equilibria in bimatrix games: a graph theoretic approach
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Thorup recently showed that single-source shortest-paths problems in undirected networks with n vertices, m edges, and edge weights drawn from {0, . . . , 2w -1} can be solved in O(n+m) time and space on a unit-cost random-access machine with a word length of w bits. His algorithm works by traversing a so-called component tree. Two new related results are provided here. First, and most importantly, Thorup's approach is generalized from undirected to directed networks. The resulting time bound, O(n + m log w), is the best deterministic linear-space bound known for sparse networks unless w is superpolynomial in log n. As an application, all-pairs shortest-paths problems in directed networks with n vertices, m edges, and edge weights in {-2w, . . . , 2w} can be solved in O(nm + n2 log log n) time and O(n + m) space (not counting the output space). Second, it is shown that the component tree for an undirected network can be constructed in deterministic linear time and space with a simple algorithm, to be contrasted with a complicated and impractical solution suggested by Thorup. Another contribution of the present paper is a greatly simplified view of the principles underlying algorithms based on component trees.