Improved Online Reachability Preservers
Greg Bodwin, Tuong Le

TL;DR
This paper introduces new online algorithms for constructing sparse reachability preservers in directed graphs, improving previous bounds and extending to stronger models, with applications to Steiner Forest problems.
Contribution
It presents polynomial-time, deterministic online constructions for reachability preservers with improved size bounds, extending to stronger models and offline settings.
Findings
Improved online reachability preserver size bounds.
Polynomial-time deterministic algorithms.
Enhanced bounds for offline and stronger models.
Abstract
A reachability preserver is a basic kind of graph sparsifier, which preserves the reachability relation of an -node directed input graph among a set of given demand pairs of size . We give constructions of sparse reachability preservers in the online setting, where is given on input, the demand pairs arrive one at a time, and we must irrevocably add edges to a preserver to ensure reachability for the pair before we can see the next demand pair. Our main results are: -- There is a construction that guarantees a maximum preserver size of This improves polynomially on the previous online upper bound of , implicit in the work of Coppersmith and Elkin [SODA '05]. -- Given a promise that the demand pairs will satisfy $P \subseteq S…
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Taxonomy
TopicsMobile Agent-Based Network Management · Access Control and Trust · Service-Oriented Architecture and Web Services
