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We present a uniform approach to design efficient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar (FRT embedding). We show how to efficiently compute an (implicit) FRT embedding in a decentralized manner and how to(More)
Massive networks arising in numerous application areas poses significant challenges for network analysts as these networks grow to billions of nodes and are prohibitively large to fit in the main memory. Finding the number of triangles in a network is an important problem in the analysis of complex networks. Several interesting graph mining applications(More)
We present a distributed algorithm that constructs an O(log n)-approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic(More)
Classification of spatial data has become important due to the fact that there are huge volumes of spatial data now available holding a wealth of valuable information. In this paper we consider the classification of spatial data streams, where the training dataset changes often. New training data arrive continuously and are added to the training set. For(More)
The Peano Count Tree (P-tree) is a quadrant-based lossless tree representation of the original spatial data. The idea of P-tree is to recursively divide the entire spatial data, such as Remotely Sensed Imagery data, into quadrants and record the count of 1-bits for each quadrant, thus forming a quadrant count tree. Using P-tree structure, all the count(More)
Recently, there has been substantial interest in the study of various random networks as mathematical models of complex systems. As these complex systems grow larger, the ability to generate progressively large random networks becomes all the more important. This motivates the need for efficient parallel algorithms for generating such networks. Naive(More)
The main focus of this paper is the analysis of a simple randomized scheme for constructing low-weight k-connected spanning subgraphs. We first show that our scheme gives a simple approximation algorithm to construct a minimum-weight k-connected spanning subgraph in a weighted complete graph, a NP-hard problem even if the weights satisfy the triangle(More)
We describe "first principles" based methods for developing synthetic urban and national scale social contact networks. Unlike simple random graph techniques, these methods use real world data sources and combine them with behavioral and social theories to synthesize networks. We develop a synthetic population for the United States modeling every individual(More)
While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time; this makes these algorithms impractical for resource-constrained networks such as ad hoc wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy(More)