Shortest paths in Euclidean graphs
Algorithmica
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
An all pairs shortest path algorithm with expected time O(n2logn)
SIAM Journal on Computing
Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
Communications of the ACM
A computational study of efficient shortest path algorithms
Computers and Operations Research
Faster algorithms for the shortest path problem
Journal of the ACM (JACM)
A guided tour of Chernoff bounds
Information Processing Letters
Shortest path algorithms: a computational study with the C programming language
Computers and Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
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
Randomized algorithms
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
On the all-pairs shortest-path algorithm of Moffat and Takaoka
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Recent results on the single-source shortest paths problem
ACM SIGACT News
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Shortest paths in digraphs of small treewidth. Part II: optimal parallel algorithms
ESA '95 Selected papers from the third European symposium on Algorithms
Worst-case efficient priority queues
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Average-case complexity of shortest-paths problems in the vertex-potential model
Random Structures & Algorithms
Floats, integers, and single source shortest paths
Journal of Algorithms
Algorithm 360: shortest-path forest with topological ordering [H]
Communications of the ACM
Single-source shortest-paths on arbitrary directed graphs in linear average-case time
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Mathematical Methods for DNA Sequences
Mathematical Methods for DNA Sequences
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Shortest Path Algorithms: An Evaluation Using Real Road Networks
Transportation Science
SPT_L shortest path algorithms: review, new proposals and some experimental results
SPT_L shortest path algorithms: review, new proposals and some experimental results
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Goal-directed shortest-path queries using precomputed cluster distances
Journal of Experimental Algorithmics (JEA)
Speed-up techniques for shortest-path computations
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
SIAM Journal on Computing
Analyzing shortest and fastest paths with GIS and determining algorithm running time
VISUAL'05 Proceedings of the 8th international conference on Visual Information and Information Systems
Approximating the statistics of various properties in randomly weighted graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
QoS-aware automatic service composition: a graph view
Journal of Computer Science and Technology - Special issue on Community Analysis and Information Recommendation
All-pairs shortest paths in O(n2) time with high probability
Journal of the ACM (JACM)
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We study the average-case running-time of single-source shortest-path (SSSP) algorithms assuming arbitrary directed graphs with n nodes, m edges, and independent random edge weights uniformly distributed in [0,1]. We give the first label-setting and label-correcting algorithms that run in linear time O(n + m) on the average. In fact, the result for the label-setting version is even obtained for dependent edge weights. In case of independence, however, the linear-time bound holds with high probability, too.Furthermore, we propose a general method to construct graphs with random edge weights that cause large expected running times when input to many traditional SSSP algorithms. We use our method to prove lower bounds on the average-case complexity of the following algorithms: the "Bellman-Ford algorithm" [R. Bellman, Quart. Appl. Math. 16 (1958) 87-90, L.R. Ford, D.R. Fulkerson, 1963], "Pallottino's Incremental Graph algorithm" [S. Pallottino, Networks 14 (1984) 257-267], the "Threshold approach" [F. Glover, R. Glover, D. Klingman, Networks 14 (1984) 23-37, F. Glover, D. Klingman, N. Phillips, Oper. Res. 33 (1985) 65-73, F. Glover, D. Klingman, N. Phillips, R.F. Schneider, Management Sci. 31 (1985) 1106-1128], the "Topological Ordering SSSP algorithm" [A.V. Goldberg, T. Radzik, Appl. Math. Lett. 6 (1993) 3-6], the "Approximate Bucket implementation" of Dijkstra's algorithm [B.V. Cherkassky, A.V. Goldberg, T. Radzik, Math. Programming 73 (1996) 129-174], and the "Δ-Stepping algorithm" [U. Meyer, P. Sanders, 1998].