Packing In A Hypergraph



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What is Packing in a hypergraph?

In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them is a random greedy algorithm which was proposed by Joel Spencer. He used a branching process to formally prove the optimal achievable bound under some side conditions. The other algorithm is called the Rödl nibble and was proposed by Vojtěch Rödl et al. They showed that the achievable packing by the Rödl nibble is in some sense close to that of the random greedy algorithm.

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