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

Monika Henzinger, Sebastian Krinninger, Danupon Nanongkai
2017 ACM Transactions on Algorithms  
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
more » ... ) 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.
doi:10.1145/3146550 fatcat:nlk7zdqmhzcbdg2lfvvb53f4j4