Nearly optimal independence oracle algorithms for edge estimation in hypergraphs

Holger Dell; John Lapinskas; Kitty Meeks

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arXiv · 2211.03874

Nearly optimal independence oracle algorithms for edge estimation in hypergraphs

Holger Dell·John Lapinskas·Kitty Meeks

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Abstract

We study a query model of computation in which an n-vertex k-hypergraph can be accessed only via its independence oracle or via its colourful independence oracle, and each oracle query may incur a cost depending on the size of the query. In each of these models, we obtain oracle algorithms to approximately count the hypergraph's edges, and we unconditionally prove that no oracle algorithm for this problem can have significantly smaller worst-case oracle cost than our algorithms.

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Holger Dell, John Lapinskas, Kitty Meeks. 2022-11-07. Nearly optimal independence oracle algorithms for edge estimation in hypergraphs. https://arxiv.org/abs/2211.03874

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