TY - GEN
T1 - Ultra-Sparse Near-Additive Emulators
AU - Elkin, Michael
AU - Matar, Shaked
N1 - 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 -