Property Testing and Parameter Testing for Permutations

There has been great interest in deciding whether a combinatorial structure satisfies some property, or in estimating the value of some numerical function associated with this combinatorial structure, by considering only a randomly chosen substructure of sufficiently large, but constant size. These problems are called property testing and parameter testing, where a property or parameter is said to be testable if it can be estimated accurately in this way. The algorithmic appeal is evident, as, conditional on sampling, this leads to reliable constant-time randomized estimators. Our paper addresses property testing and parameter testing for permutations in a subpermutation perspective; more precisely, we investigate permutation properties and parameters that can be wellapproximated based on randomly chosen subpermutations of much smaller size. In this context, we give a permutation counterpart of a famous result by Alon and Shapira [6] stating that every hereditary graph property is tes...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Carlos Hoppen, Yoshiharu Kohayakawa, Carlos G. T. de A. Moreira, Rudini M. Sampaio
• Keywords: Discrete Algorithms, Parameter Testing, Permutation Counterpart, SODA 2010, Testable Permutation Parameters