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

Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks…

Load balance is important for MapReduce to reduce job duration, increase parallel efficiency, etc. Previous work focuses on coarse-grained scheduling. This study concerns fine-grained scheduling on MapReduce operations. Each operation…

We introduce dynamic smooth (a.k.a. balanced) compressed quadtrees with worst-case constant time updates in constant dimensions. We distinguish two versions of the problem. First, we show that quadtrees as a space-division data structure…

The Wasserstein distance is a discrepancy measure between probability distributions, defined by an optimal transport problem. It has been used for various tasks such as retrieving similar items in high-dimensional images or text data. In…

Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…

Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…

In this paper we propose an online approximate k-nn graph building algorithm, which is able to quickly update a k-nn graph using a flow of data points. One very important step of the algorithm consists in using the current distributed graph…

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…

An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…

Manipulating downward-closed sets of vectors forms the basis of so-called antichain-based algorithms in verification. In that context, the dimension of the vectors is intimately tied to the size of the input structure to be verified. In…

We propose a novel tree-like curvilinear structure reconstruction algorithm based on supervised learning and graph theory. In this work we analyze image patches to obtain the local major orientations and the rankings that correspond to the…

Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…

We study the fundamental problem of distributed network formation among mobile agents of limited computational power that aim to achieve energy balance by wirelessly transmitting and receiving energy in a peer-to-peer manner. Specifically,…

In this paper, we provide algorithms to rank and unrank certain degree-restricted classes of Cayley trees (spanning trees of the n-vertex complete graph). Specifically, we consider classes of trees that have a given set of leaves or a fixed…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

A data structure, called a biased range tree, is presented that preprocesses a set S of n points in R^2 and a query distribution D for 2-sided orthogonal range counting queries. The expected query time for this data structure, when queries…

Given a subset of active nodes in a network can we re- construct the cascade that has generated these observa- tions? This is a problem that has been studied in the literature, but here we focus in the case that tempo- ral information is…

Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We…

We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements…

Augmentation makes search trees tremendously more versatile, allowing them to support efficient aggregation queries, order-statistic queries, and range queries in addition to insertion, deletion, and lookup. In this paper, we present the…