相关论文: Building a Balanced k-d Tree with MapReduce

Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…

The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…

In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…

In [1], a new construction called red-black hierarchy characterizing Laman graphs and an algorithm for computing it were presented. For a Laman graph G=(V,E) with n vertices it runs in O(n^2) time assuming that a partition of (V,E+e) into…

In this paper, we address the problem of enumerating all induced subtrees in an input k-degenerate graph, where an induced subtree is an acyclic and connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for any its…

Erikkson showed that singular value decomposition(SVD) of flattenings determined a partition of a phylogenetic tree to be a split. In this paper, based on his work, we develop new statistically consistent algorithms fit for grid computing…

In a reconfiguration problem, given a problem and two feasible solutions of the problem, the task is to find a sequence of transformations to reach from one solution to the other such that every intermediate state is also a feasible…

MapReduce framework is the de facto in big data and its applications where a big data-set is split into small data chunks that are replicated on different servers among thousands of servers. The heterogeneous server structure of the system…

This paper presents a novel algorithm, called MRRT, which uses multiple rapidly-exploring random trees for fast online replanning of autonomous vehicles in dynamic environments with moving obstacles. The proposed algorithm is built upon the…

Classification data sets with skewed class proportions are called imbalanced. Class imbalance is a problem since most machine learning classification algorithms are built with an assumption of equal representation of all classes in the…

We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…

The Minimum Size Tree Decomposition (MSTD) and Minimum Size Path Decomposition (MSPD) problems ask for a given n-vertex graph G and integer k, what is the minimum number of bags of a tree decomposition (respectively, path decomposition) of…

We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…

A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…

We present a simple randomized incremental algorithm for building compressed quadtrees. The resulting algorithm seems to be simpler than previously known algorithms for this task.

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…

In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes. This is motivated from computational biology, data protection, and computer…