We study Ramsey-theoretic properties of several natural classes of finite ultrametric spaces, describe the corresponding Urysohn spaces and compute a dynamical invariant attached to their isometry groups.

We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is D-equivalent to an ultrametric, where D ∈ (2,∞) is a prescribed target distortion. Since this procedure works for D arbitrarily close to the nonlinear Dvoretzky phase transition at distortion 2, we thus obtain a much simpler probabilistic pro...

We study the problem of computing a low-distortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M ′ with minimum multiplicative distortion. This problem arises naturally in many applications, including geometric optimization, visualization, multi-dimensional scaling, network spa...

We study active learning of classes of recursive functions by asking value queries about the target function f , where f is from the target class. That is, the query is a natural number x, and the answer to the query is f(x). The complexity measure in this paper is the worst-case number of queries asked. We prove that for some classes of recursive functions ultrametric active learning algorithm...

The L p-min increment t and L p-min increment ultrametric t problems are two popular optimization problems arising from distance methods for reconstructing phyloge-netic trees. This paper gives the following results: 1. An O(n 2) approximation algorithm with ratio-3 for L 1-min increment t. 2. A ratio-O(n 1=p) approximation algorithm for L p-min increment ultrametric t. 3. The neighbor-joining ...

Coding of data, usually upstream of data analysis, has crucial implications for the data analysis results. By modifying the data coding – through use of less than full precision in data values – we can aid appreciably the effectiveness and efficiency of the hierarchical clustering. In our first application, this is used to lessen the quantity of data to be hierarchically clustered. The approach...

A Parallel Frequent Item sets mining algorithm called FiDoop using MapReduce programming model. FiDoop includes the frequent items ultrametric tree(FIU-tree), in that three MapReduce jobs are applied to complete the mining task. The scalability problem has been addressed bythe implementation of a handful of FP-growth-like parallelFIM algorithms. InFiDoop, the mappers independently and concurren...