On Computing the Frequencies of Induced Subhypergraphs

Let F be an r-uniform hypergraph with f vertices, where f > r ≥ 3. In [12], R. Yuster posed the problem of whether there exists an algorithm which, for a given r-uniform hypergraph H with n vertices, computes the number of induced copies of F in H in time o(nf ). The analogous question for graphs (r = 2) was known to hold from a O(nf−ε ) time algorithm of Neˇsetˇril and Poljak [9] (for a constant ε = εf > 0 which is independent of n). Here, we present an algorithm for this problem, when r ≥ 3, with running time O(nf / log2 n).

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Brendan Nagle
• Keywords: Algorithm, Analogous Question, R-uniform Hypergraph, SIAMDM 2010