Year: 2022
Type: preprint
Abstract: Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in $O (D \log\log n + \log^3 n)$ rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in $O (D \log^2 n + \log^3 n)$ rounds with high probability. Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the (polynomially-large) hyperedge set of a hypergraph $H = (V_H, E_H)$ into $k = Θ(\log^2 n)$ disjoint subsets $F_1 \cup \cdots \cup F_k = E_H$ such that the (sub-)hypergraph $(V_H, F_i)$ is bipartite in the sense that there exists a vertex subset $U \subseteq V$ such that $|U \cap e| = 1$ for every $e \in F_i$. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.
Source: arXiv (Cornell University)
Authors: Dufoulon, Fabien, Emek, Yuval, Gelles, Ran
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: CCF-BSF: AF:Small: Time-Message Tradeoffs in Distributed Algorithms, BIGDATA: Collaborative Research: F: Efficient Distributed Computation of Large-Scale Graph Problems in Epidemiology and Contagion Dynamics, G5943845093, AI Institute: Planning: Novel Neural Architectures for 4D Materials Science, BSF:2014424:Time-Message Tradeoffs in Distributed Algorithms
OpenAlex ID: W4306309371