DocumentCode :
1711519
Title :
All-Pairs Shortest Paths in O(n²) Time with High Probability
Author :
Peres, Yuval ; Sotnikov, Dmitry ; Sudakov, Benny ; Zwick, Uri
fYear :
2010
Firstpage :
663
Lastpage :
672
Abstract :
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0,1] is O(n2), in expectation and with high probability. This resolves a long standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano. The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n2), in expectation and with high probability. We also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in O(log2 n) expected time.
Keywords :
computational complexity; directed graphs; probability; complete directed graph; dynamic all-pairs shortest paths algorithm; edge weights; high probability; long standing open problem; running time; Algorithm design and analysis; Data structures; Harmonic analysis; Heuristic algorithms; Probabilistic logic; Random variables; Upper bound; graph algorithms; random graphs; shortest paths;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on
Conference_Location :
Las Vegas, NV
ISSN :
0272-5428
Print_ISBN :
978-1-4244-8525-3
Type :
conf
DOI :
10.1109/FOCS.2010.69
Filename :
5671327
Link To Document :
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