# Ultra-Sparse Near-Additive Emulators

@article{Elkin2021UltraSparseNE, title={Ultra-Sparse Near-Additive Emulators}, author={Michael Elkin and Shaked Matar}, journal={Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing}, year={2021} }

Near-additive (aka (1+ε,β)β-) emulators and spanners are a fundamental graph-algorithmic construct, with numerous applications for computing approximate shortest paths and related problems in distributed, streaming and dynamic settings. Known constructions of near-additive emulators enable one to trade between their sparsity (i.e., number of edges) and the additive stretch β. Specifically, for any pair of parameters ε >0, κ=1,2,..., one can have a (1+ε,β)-emulator with O(n^1+1/κ ) edges, with…

## One Citation

Deterministic Distributed Algorithms and Lower Bounds in the Hybrid Model

- Computer ScienceDISC
- 2021

This work presents a deterministic algorithm which solves any problem on a sparse n-node graph in Õ( √ n) rounds of HYBRID, and proves via a reduction from the set disjointness problem that Ω̃(n1/3) rounds are required to determine the radius of an unweighted graph, as well as a (3/2 − ε)-approximation for weighted graphs.

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