ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A simple solution to the k-core problem
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
The k-orientability thresholds for Gn, p
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Maximum matching in sparse random graphs
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Weighted enumeration of spanning subgraphs with degree constraints
Journal of Combinatorial Theory Series B
Information, Physics, and Computation
Information, Physics, and Computation
Load balancing and orientability thresholds for random hypergraphs
Proceedings of the forty-second ACM symposium on Theory of computing
Proceedings of the 37th international colloquium conference on Automata, languages and programming
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Tight thresholds for cuckoo hashing via XORSAT
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Orientability of random hypergraphs and the power of multiple choices
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The multiple-orientability thresholds for random hypergraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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A h-uniform hypergraph H = (V, E) is called (l, k)-orientable if there exists an assignment of each hyper-edge e ε to exactly l of its vertices v ε 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.