Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The algorithmic aspects of the regularity lemma
Journal of Algorithms
A Fast Approximation Algorithm for Computing theFrequencies of Subgraphs in a Given Graph
SIAM Journal on Computing
Extremal problems on set systems
Random Structures & Algorithms
On characterizing hypergraph regularity
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
An Optimal Algorithm for Checking Regularity
SIAM Journal on Computing
Finding and counting cliques and independent sets in r-uniform hypergraphs
Information Processing Letters
An Algorithmic Version of the Hypergraph Regularity Method
SIAM Journal on Computing
Hypergraph regularity and quasi-randomness
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
| Hi-index | 0.00 |
Let $\mathcal{F}$ be an $r$-uniform hypergraph with $f$ vertices, where $fr\geq3$. In [Inform. Process. Lett., 99 (2006), pp. 130-134], Yuster posed the problem of whether there exists an algorithm which, for a given $r$-uniform hypergraph $\mathcal{H}$ with $n$ vertices, computes the number of induced copies of $\mathcal{F}$ in $\mathcal{H}$ in time $o(n^f)$. The analogous question for graphs ($r=2$) was known to hold from an $O(n^{f-\varepsilon})$ time algorithm of Nešetřil and Poljak [Comment. Math. Univ. Carolin., 26 (1985), pp. 415-419] (for a constant $\varepsilon=\varepsilon_f0$ which is independent of $n$). Here, we present an algorithm for this problem, when $r\geq3$, with running time $O(n^f/\log_2n)$.