The complexity of ultrametric partitions on graphs
Information Processing Letters
A fast algorithm for constructing trees from distance matrices
Information Processing Letters
Determining the evolutionary tree using experiments
Journal of Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)
SIAM Journal on Computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Property testing of data dimensionality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Abstract Combinatorial Programs and Efficient Property Testers
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
SIAM Journal on Discrete Mathematics
FIUT: A new method for mining frequent itemsets
Information Sciences: an International Journal
On proximity oblivious testing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
On Proximity-Oblivious Testing
SIAM Journal on Computing
| Hi-index | 0.00 |
Finite metric spaces, and in particular tree metrics play an important role in various disciplines such as evolutionary biology and statistics. A natural family of problems concerning metrics is deciding, given a matrix M, whether or not it is a distance metric of a certain predetermined type. Here we consider the following relaxed version of such decision problems: For any given matrix M and parameter ε, we are interested in determining, by probing M, whether M has a particular metric property P, or whether it is ε-far from having the property. In ε-far we mean that at least an ε-fraction of the entries of M must be modified so that it obtains the property. The algorithm may query the matrix on entries M[i,j] of its choice, and is allowed a constant probability of error.We describe algorithms for testing Euclidean metrics, tree metrics and ultrametrics. Furthermore, we present an algorithm that tests whether a matrix M is an approximate ultrametric. In all cases the query complexity and running time are polynomial in 1/ε and independent of the size of the matrix. Finally, our algorithms can be used to solve relaxed versions of the corresponding search problems in time that is sub-linear in the size of the matrix.