Chenglin Fan

We study the problem of merging decision trees: Given k decision trees $T_1,T_2,T_3...,T_k$, we merge these trees into one super tree T with (often) much smaller size. The resultant super tree T, which is an integration of k decision trees with each leaf having a major label, can also be considered as a (lossless) compression of a random forest. For any testing instance, it is guaranteed that the tree T gives the same prediction as the random forest consisting of $T_1,T_2,T_3...,T_k$ but it save

Metric data plays an important role in various settings, for example, in metric-based indexing, clustering, classification, and approximation algorithms in general. Due to measurement error, noise, or an inability to completely gather all the data, a collection of distances may not satisfy the basic metric requirements, most notably the triangle inequality. In this paper we initiate the study of the metric violation distance problem: given a set of pairwise distances, modify the minimum number o

Data about individuals may contain private and sensitive information. The differential privacy (DP) was proposed to address the problem of protecting the privacy of each individual while keeping useful information about a population. Sealfon [1] introduced a private graph model in which the graph topology is assumed to be public while the weight information is assumed to be private. That model can express hidden congestion patterns in a known transportation system. In this paper, we revisit the

In normal Voronoi diagram, each site is able to see all points in the plane. In this paper, we study the problem such that each site is only able to see half-plane and construct the so-called Half-plane Voronoi Diagram (HPVD). We show that the half-plane Voronoi cell of each site is not necessary convex and it could consist of many disjoint regions. We prove that the complexity of the HPVD of n sites is $O(n^2)$. Then we give an algorithm of $O(n\log n)$ time and $O(n)$ space to construct HPVD s

Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimension reduction. As real data sets are noisy, distances often fail to satisfy a metric. For this reason, Gilbert and Jain and Fan et al. introduced the closely related sparse metric repair and metric violation distance problems. The goal of these problems is to repair as few distances as poss

Releasing all pairwise shortest path (APSP) distances between vertices on general graphs under weight Differential Privacy (DP) is known as a challenging task. In the previous attempt of (Sealfon 2016}, by adding Laplace noise to each edge weight or to each output distance, to achieve DP with some fixed budget, with high probability the maximal absolute error among all published pairwise distances is roughly $O(n)$ where $n$ is the number of nodes. It was shown that this error could be reduced f

We study the problem of moving network Voronoi diagram: given a network with n nodes and E edges. Suppose there are m sites (cars, postmen, etc) moving along the network edges, we design the algorithms to compute the dynamic network Voronoi diagram as sites move such that we can answer the nearest neighbor query efficiently. Furthermore, we extend it to the k-order dynamic network Voronoi diagram such that we can answer the k nearest neighbor query efficiently. We also study the problem when the

Measuring the similarity of two polygonal curves is a fundamental computational task. Among alternatives, the Frechet distance is one of the most well studied similarity measures. Informally, the Fréchet distance is described as the minimum leash length required for a man on one of the curves to walk a dog on the other curve continuously from the starting to the ending points. In this paper we study a variant called the Fréchet gap distance. In the man and dog analogy, the Fréchet gap distance m