Learning a hidden hypergraph

• Authors: Dana Angluin;Jiang Chen
• Venue: COLT'05 Proceedings of the 18th annual conference on Learning Theory
• Year: 2005

We consider the problem of learning a hypergraph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden hypergraph or not. We show that an r-uniform hypergraph with m edges and n vertices is learnable with O(2$^{\rm 4{\it r}}$m · poly(r,log n)) queries with high probability. The queries can be made in O(min(2rr2 log2n, r3 log3n)) rounds. We also give an algorithm that learns a non-uniform hypergraph whose minimum edge size is r1 and maximum edge size is r2 using $O(f_{1}(r_{1},r_{2})\cdot m^{(r_{2}-r_{1}+2)/2} \cdot poly(log n))$ queries with high probability, and give a lower bound of $\Omega(f_{2}(r_{1},r_{2})\cdot m^{(r_{2}-r_{1}+2)/2})$ for this class of hypergraphs, where f1 and f2 are functions depending only on r1 and r2. The queries can also be made in $O(min(2^{r2}r^{2}_{2}log^{2} n,r^{3}_{2}log^{3}n))$ rounds.