TY - GEN

T1 - Ultra-Sparse Near-Additive Emulators

AU - Elkin, Michael

AU - Matar, Shaked

N1 - Funding Information:
This research was supported by the ISF grant No. (2344/19).
Publisher Copyright:
© 2021 ACM.

PY - 2021/7/21

Y1 - 2021/7/21

N2 - 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(n1+1/κ ) edges, with β = łeft(\fracłog κ ϵ \right)łog κ . At their sparsest, these emulators employ c.n edges, for some constant c≥ 2. We tighten this bound, and show that in fact precisely n1+1/κ edges suffice.

AB - 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(n1+1/κ ) edges, with β = łeft(\fracłog κ ϵ \right)łog κ . At their sparsest, these emulators employ c.n edges, for some constant c≥ 2. We tighten this bound, and show that in fact precisely n1+1/κ edges suffice.

KW - deterministic

KW - distributed algorithms

KW - emulators

UR - http://www.scopus.com/inward/record.url?scp=85112371659&partnerID=8YFLogxK

U2 - 10.1145/3465084.3467926

DO - 10.1145/3465084.3467926

M3 - Conference contribution

AN - SCOPUS:85112371659

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 235

EP - 246

BT - PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021

Y2 - 26 July 2021 through 30 July 2021

ER -