# Distributed Distance Approximation

@article{Ancona2020DistributedDA,
title={Distributed Distance Approximation},
author={Bertie Ancona and Keren Censor-Hillel and Mina Dalirrooyfard and Yuval Efron and Virginia Vassilevska Williams},
journal={ArXiv},
year={2020},
volume={abs/2011.05066}
}
Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact solutions. In this paper, we give a near complete characterization of the trade-offs between approximation ratios and round complexity of distributed algorithms for approximating these parameters, with a focus on the weighted and directed variants. Furthermore, we… Expand
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#### References

SHOWING 1-10 OF 59 REFERENCES
Towards tight approximation bounds for graph diameter and eccentricities
• Mathematics, Computer Science
• STOC
• 2018
The lower bound for near-linear time algorithms is essentially tight by giving an algorithm that approximates Eccentricities within a 2+δ factor in Õ(m/δ) time for any 0<δ<1, which is the first lower bound in fine-grained complexity that addresses near- linear time computation. Expand
Approximation and Fixed Parameter Subquadratic Algorithms for Radius and Diameter in Sparse Graphs
• Computer Science, Mathematics
• SODA
• 2016
Truly subquadratic approximation algorithms for most of the versions of Diameter and Radius with optimal approximation guarantees are found, under plausible assumptions, since even a $(3/2-\delta)$-approximation algorithm that runs in time $2^{o(k)n 2-\epsilon}$ would refute the plausible assumptions. Expand
Near-Linear Lower Bounds for Distributed Distance Computations, Even in Sparse Networks
• Computer Science
• DISC
• 2016
A new technique for constructing sparse graphs that allow us to prove near-linear lower bounds on the round complexity of computing distances in the CONGEST model and shows an $\widetilde{\Omega}(n)$ lower bound for computing the diameter in sparse networks. Expand
New Bounds for Approximating Extremal Distances in Undirected Graphs
• Computer Science, Mathematics
• SODA
• 2016
New bounds are provided for the approximation of extremal distances (the diameter, the radius, and the eccentricities of all nodes) of an undirected graph with n nodes and m edges and an algorithmic scheme gives a family of previously unknown bounds. Expand
Distributed Algorithms for Network Diameter and Girth
• Mathematics, Computer Science
• ICALP
• 2012
A distributed algorithm that computes the diameter of the network in O(n) rounds and two distributed approximation algorithms that almost match their lower bounds for constant diameter and for constant girth. Expand
Distributed Spanner Approximation
• Mathematics, Computer Science
• PODC
• 2018
This work addresses the fundamental network design problem of constructing approximate minimum spanners with a new distributed construction of minimum 2-spanners that uses only polynomial local computations and provides a Congest algorithm for the minimum dominating set problem, with a guaranteed O(log Δ) approximation ratio. Expand
Fast Approximate Shortest Paths in the Congested Clique
• Computer Science
• PODC
• 2019
The main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which the authors leverage to construct efficient hopsets and shortest paths and an exact single-source shortest paths algorithm for weighted undirected graphs in Õ (n1/6) rounds. Expand
Smaller Cuts, Higher Lower Bounds
• Computer Science
• ACM Trans. Algorithms
• 2021
This paper proves strong lower bounds for distributed computing in the CONGEST model, by presenting the bit-gadget: a new technique for constructing graphs with small cuts, and it is shown that graph constructions forCONGEST lower bounds translate toLower bounds for the semi-streaming model, despite being very different in its nature. Expand
A note on hardness of diameter approximation
• Mathematics, Computer Science
• Inf. Process. Lett.
• 2018
The hardness of approximating the diameter of a network is revisited and the connection to orthogonal vectors explicit is made, leading to a conceptually more streamlined exposition. Expand
Further Algebraic Algorithms in the Congested Clique Model and Applications to Graph-Theoretic Problems
• F. Gall
• Computer Science, Mathematics
• DISC
• 2016
Deterministic and randomized algorithms are presented, in the congested clique model, for efficiently computing multiple independent instances of matrix products, computing the determinant, the rank and the inverse of a matrix, and solving systems of linear equations. Expand