This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far apart locations, the algorithms use additional mechanisms compared to their sequential counterparts. We complement our algorithms with a lower bound on the number of rounds required for computing pairwise spanners. The standard reductions from set-disjointness and equality seem unsuitable for this task because no specific edge needs to be removed from the graph. Instead, to obtain our lower bound, we define a new communication complexity problem that reduces to computing a sparse spanner, and prove a lower bound on its communication complexity. This technique significantly extends the current toolbox used for obtaining
Several lower bounds for the time complexity of spanner construction in the congest model where presented in REF , but these are applicable only to pairwise spanners with a bounded number of pairs, and not to all-pairs spanners.
Distributed construction of purely additive spanners
Distributed Computing
Distributed Computing
Mathematics Computer Science Engineering