All-pairs shortest paths in O(n2) time with high probability


METADATA ONLY
Loading...

Date

2013-08

Publication Type

Journal Article

ETH Bibliography

no

Citations

Altmetric
METADATA ONLY

Data

Rights / License

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 [2006]. 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(log2n) expected time.

Publication status

published

Editor

Book title

Volume

60 (4)

Pages / Article No.

26

Publisher

Association for Computing Machinery

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

Organisational unit

03993 - Sudakov, Benjamin / Sudakov, Benjamin check_circle

Notes

Funding

Related publications and datasets