@inproceedings{fd96680be1d448fbb95a7148a5b2d892,
title = "All-pairs shortest paths in O(n2) time with high probability",
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(n 2), 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 = "Graph algorithms, Shortest paths",
author = "Yuval Peres and Dmitry Sotnikov and Benny Sudakov and Uri Zwick",
year = "2010",
doi = "10.1109/FOCS.2010.69",
language = "אנגלית",
isbn = "9780769542447",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "663--672",
booktitle = "Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010",
address = "ארצות הברית",
note = "2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 ; Conference date: 23-10-2010 Through 26-10-2010",
}