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- W2952096314 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2012 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)A New Approach to the Orientation of Random HypergraphsM. LelargeM. Lelargepp.251 - 264Chapter DOI:https://doi.org/10.1137/1.9781611973099.23PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract A h-uniform hypergraph H = (V, E) is called (ℓ, k)-orientable if there exists an assignment of each hyperedge e ∊ E to exactly ℓ of its vertices v ∊ e such that no vertex is assigned more than k hyperedges. Let Hn,m,h be a hypergraph, drawn uniformly at random from the set of all h-uniform hypergraphs with n vertices and m edges. In this paper, we determine the threshold of the existence of a (ℓ, k)-orientation of Hn,m,h for k > 1 and h > ℓ > 1, extending recent results motivated by applications such as cuckoo hashing or load balancing with guaranteed maximum load. Our proof combines the local weak convergence of sparse graphs and a careful analysis of a Gibbs measure on spanning subgraphs with degree constraints. It allows us to deal with a much broader class than the uniform hypergraphs. Previous chapter Next chapter RelatedDetails Published:2012ISBN:978-1-61197-210-8eISBN:978-1-61197-309-9 https://doi.org/10.1137/1.9781611973099Book Series Name:ProceedingsBook Code:PR141Book Pages:xiii + 1757" @default.
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- W2952096314 date "2012-01-17" @default.
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- W2952096314 title "A New Approach to the Orientation of Random Hypergraphs" @default.
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