Fast Distributed Backup Placement in Sparse and Dense Networks
Leonid Barenboim, Gal Oren

TL;DR
This paper presents fast, deterministic distributed algorithms for the backup placement problem in various network topologies, achieving near-optimal or optimal solutions in constant or logarithmic rounds.
Contribution
It introduces new algorithms with improved round complexity for backup placement in specific graph classes, including constant-time solutions for graphs with bounded neighborhood independence and near-optimal solutions for sparse graphs.
Findings
Constant-time algorithms for graphs with bounded neighborhood independence.
Logarithmic-round algorithms for sparse graphs like trees and planar graphs.
Lower bounds showing the near-optimality of the proposed algorithms.
Abstract
We consider the Backup Placement problem in networks in the distributed setting. Given a network graph , the goal of each vertex is selecting a neighbor, such that the maximum number of vertices in that select the same vertex is minimized. The backup placement problem was introduced by Halldorsson, Kohler, Patt-Shamir, and Rawitz, who obtained an approximation with randomized polylogarithmic time. Their algorithm remained the state-of-the-art for general graphs, as well as specific graph topologies. In this paper we obtain significantly improved algorithms for various graph topologies. Specifically, we show that -approximation to optimal backup placement can be computed deterministically in rounds in graphs that model wireless networks, certain social networks, claw-free graphs, and more generally, in any…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Mobile Ad Hoc Networks · Privacy-Preserving Technologies in Data
