Related papers: Optimal-Length Labeling Schemes and Fast Algorithm…
Inspired by the great success of machine learning in the past decade, people have been thinking about the possibility of improving the theoretical results by exploring data distribution. In this paper, we revisit a fundamental problem…
We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and…
The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…
The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
Over the years, much research involving mobile computational entities has been performed. From modeling actual microscopic (and smaller) robots, to modeling software processes on a network, many important problems have been studied in this…
We consider $K$-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering…
The best known solutions for $k$-message broadcast in dynamic networks of size $n$ require $\Omega(nk)$ rounds. In this paper, we see if these bounds can be improved by smoothed analysis. We study perhaps the most natural randomized…
We consider distributed optimization over a $d$-dimensional space, where $K$ remote clients send coded gradient estimates over an {\em additive Gaussian Multiple Access Channel (MAC)} with noise variance $\sigma_z^2$. Furthermore, the…
We present scalable parallel algorithms with sublinear per-processor communication volume and low latency for several fundamental problems related to finding the most relevant elements in a set, for various notions of relevance: We begin…
We consider the scenario of $n$ sensor nodes observing streams of data. The nodes are connected to a central server whose task it is to compute some function over all data items observed by the nodes. In our case, there exists a total order…
In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a…
In this paper, we present a distributed algorithm which implements the $k$-means algorithm in a distributed fashion for multi-agent systems with directed communication links. The goal of $k$-means is to partition the network's agents in…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…
The mobile robot dispersion problem on graphs asks $k\leq n$ robots placed initially arbitrarily on the nodes of an $n$-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of…
We study the problem of partitioning a small sample of $n$ individuals from a mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according to their distributions. Each distribution is described by a vector of allele…
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
The number of nodes of a network, called its size, and the largest distance between nodes of a network, called its diameter, are among the most important network parameters. Knowing the size and/or diameter is a prerequisite of many…