eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-01
45:1
45:24
10.4230/LIPIcs.ITCS.2023.45
article
Beeping Shortest Paths via Hypergraph Bipartite Decomposition
Dufoulon, Fabien
1
https://orcid.org/0000-0003-2977-4109
Emek, Yuval
2
https://orcid.org/0000-0002-3123-3451
Gelles, Ran
3
https://orcid.org/0000-0003-3615-3239
Department of Computer Science, University of Houston, TX, USA
Technion, Haifa, Israel
Bar-Ilan University, Ramat-Gan, Israel
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 + log³ n) rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in O(D log² n + log³ 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 hyperedge set of a hypergraph H = (V_H, E_H) into k = Θ (log² n) disjoint subsets F₁ ∪ ⋯ ∪ 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 ⊆ V such that |U ∩ e| = 1 for every e ∈ F_i. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol251-itcs2023/LIPIcs.ITCS.2023.45/LIPIcs.ITCS.2023.45.pdf
Beeping Networks
Shortest Paths
Hypergraph Bipartite Decomposition