@inproceedings{65de883b2e1747e7a489d242f2e24478,

title = "Beeping Shortest Paths via Hypergraph Bipartite Decomposition",

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 + 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 = (VH, EH) into k = Θ(log2 n) disjoint subsets F1 ∪ · · · ∪ Fk = EH such that the (sub-)hypergraph (VH, Fi) is bipartite in the sense that there exists a vertex subset U ⊆ V such that |U ∩ e| = 1 for every e ∈ Fi. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.",

keywords = "Beeping Networks, Hypergraph Bipartite Decomposition, Shortest Paths",

author = "Fabien Dufoulon and Yuval Emek and Ran Gelles",

note = "Publisher Copyright: {\textcopyright} Fabien Dufoulon, Yuval Emek, and Ran Gelles; licensed under Creative Commons License CC-BY 4.0.; 14th Innovations in Theoretical Computer Science Conference, ITCS 2023 ; Conference date: 10-01-2023 Through 13-01-2023",

year = "2023",

month = jan,

day = "1",

doi = "10.4230/LIPIcs.ITCS.2023.45",

language = "אנגלית",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

editor = "Kalai, {Yael Tauman}",

booktitle = "14th Innovations in Theoretical Computer Science Conference, ITCS 2023",

}