Testing metric properties
Michal Parnas, Dana Ron · 2001
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 \eps, 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 more than 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.