Nearly optimal independence oracle algorithms for edge estimation in hypergraphs

TL;DR

This paper develops nearly optimal algorithms for estimating the number of edges in hypergraphs using independence oracles, establishing bounds on the query complexity in these models.

Contribution

It introduces new oracle algorithms for hypergraph edge estimation and proves their near-optimality in terms of worst-case oracle cost.

Findings

Algorithms achieve near-optimal edge count estimation

Unconditional lower bounds match the algorithms' complexity

Applicable to models with independence and colourful independence oracles

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.