Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic (1+ϵ)-approximation algorithms whose amortized time (over some nu...
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Veröffentlicht in: | ACM transactions on algorithms 2017-12, Vol.13 (4), p.1-24 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We study the problem of maintaining a
breadth-first spanning tree
(BFS tree) in
partially dynamic
distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic (1+ϵ)-approximation algorithms whose amortized time (over some number of link changes) is
sublinear
in
D
, the
maximum diameter
of the network.
Our technique also leads to a deterministic (1+ϵ)-approximate incremental algorithm for single-source shortest paths in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic
exact
algorithm of Even and Shiloach (1981), which is optimal under some assumptions (Roditty and Zwick 2011; Henzinger et al. 2015). Our result is the first to show that, in the incremental setting, this bound can be beaten in certain cases if some approximation is allowed. |
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ISSN: | 1549-6325 1549-6333 1549-6333 |
DOI: | 10.1145/3146550 |