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arXiv · 1512.08147

Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks

Monika Henzinger·Sebastian Krinninger·Danupon Nanongkai
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Abstract

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 $(1+\epsilon)$-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 $(1+\epsilon)$-approximate incremental algorithm for single-source shortest paths (SSSP) in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic exact algorithm of Even and Shiloach [JACM 1981] that is optimal under some assumptions [Roditty and Zwick ESA 2004, Henzinger et al. STOC 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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Monika Henzinger, Sebastian Krinninger, Danupon Nanongkai. 2015-12-26. Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks. https://doi.org/10.1145/3146550

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