Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Relational properties expressible with one universal quantifier are testable
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Hardness and algorithms for rainbow connection
Journal of Combinatorial Optimization
Introduction to testing graph properties
Property testing
Introduction to testing graph properties
Property testing
Introduction to testing graph properties
Studies in complexity and cryptography
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
We show that any partition-problem of hypergraphs has an O(n) time approximate partitioning algorithm and an efficient property tester. This extends the results of Goldreich, Goldwasser and Ron who obtained similar algorithms for the special case of graph partition problems in their seminal paper [16]. The partitioning algorithm is used to obtain the following results: We derive a surprisingly simple O(n) time algorithmic version of Szemerédi's regularity lemma. Unlike all the previous approaches for this problem [3, 10, 14, 15, 21], which only guaranteed to find partitions of towersize, our algorithm will find a small regular partition in the case that one exists; For any r \geqslant 3, we give an O(n) time randomized algorithm for constructing regular partitions of r-uniform hypergraphs, thus improving the previous {\rm O}(n^{2r - 1}) time (deterministic) algorithms [8, 15]. The property testing algorithm is used to unify several previous results, and to obtain the partition densities for the above problems (rather than the partitions themselves) using only poly(1/ \in ) queries and constant running time.