Maleq Khan

Distributed Algorithms for Constructing Approximate Minimum Spanning Trees in Wireless Sensor Networks

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 efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called nearest neighbor tree (NNT) algorithms for energy-efficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate the theoretical results and show that the bounds are much better in practice.

Generation and analysis of large synthetic social contact networks

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 in the population including household structure, demographics and a 24-hour activity sequence. The process involves collecting and manipulating public and proprietary data sets integrated into a common architecture for data exchange and then using these data sets to generate new relations. A social contact network is derived from the synthetic population based on physical co-location of interacting persons. We use graph measures to compare and contrast the structural characteristics of the social networks that span different urban regions. We then simulate diffusion processes on these networks and analyze similarities and differences in the structure of the networks.

k-nearest Neighbor Classification on Spatial Data Streams Using P-trees

Classification of spatial data streams is crucial, since the training dataset changes often. Building a new classifier each time can be very costly with most techniques. In this situation, k-nearest neighbor (KNN) classification is a very good choice, since no residual classifier needs to be built ahead of time. KNN is extremely simple to implement and lends itself to a wide variety of variations. We propose a new method of KNN classification for spatial data using a new, rich, data-mining-ready structure, the Peano-count-tree (P-tree). We merely perform some AND/OR operations on P-trees to find the nearest neighbors of a new sample and assign the class label. We have fast and efficient algorithms for the AND/OR operations, which reduce the classification time significantly. Instead of taking exactly the k nearest neighbors we form a closed-KNN set. Our experimental results show closed-KNN yields higher classification accuracy as well as significantly higher speed.

PATRIC: a parallel algorithm for counting triangles in massive networks

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 depend on the number of triangles in the graph. In this paper, we present an efficient MPI-based distributed memory parallel algorithm, called PATRIC, for counting triangles in massive networks. PATRIC scales well to networks with billions of nodes and can compute the exact number of triangles in a network with one billion nodes and 10 billion edges in 16 minutes. Balancing computational loads among processors for a graph problem like counting triangles is a challenging issue. We present and analyze several schemes for balancing load among processors for the triangle counting problem. These schemes achieve very good load balancing. We also show how our parallel algorithm can adapt an existing edge sparsification technique to approximate the number of triangles with very high accuracy. This modification allows us to count triangles in even larger networks.

The P-tree algebra

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 information can be calculated quickly. This facilitates efficient ways for data mining. In this paper, we will focus on the algebra and properties of P-tree structure and its variations. We have implemented fast algorithms for P-tree generation and P-tree operations. Our performance analysis shows P-tree has small space and time costs compared to the original data. We have also implemented some data mining algorithms using P-trees, such as Association Rule Mining, Decision Tree Classification and K-Clustering.

SAHAD: Subgraph Analysis in Massive Networks Using Hadoop

Relational sub graph analysis, e.g. finding labeled sub graphs in a network, which are isomorphic to a template, is a key problem in many graph related applications. It is computationally challenging for large networks and complex templates. In this paper, we develop SAHAD, an algorithm for relational sub graph analysis using Hadoop, in which the sub graph is in the form of a tree. SAHAD is able to solve a variety of problems closely related with sub graph isomorphism, including counting labeled/unlabeled sub graphs, finding supervised motifs, and computing graph let frequency distribution. We prove that the worst case work complexity for SAHAD is asymptotically very close to that of the best sequential algorithm. On a mid-size cluster with about 40 compute nodes, SAHAD scales to networks with up to 9 million nodes and a quarter billion edges, and templates with up to 12 nodes. To the best of our knowledge, SAHAD is the first such Hadoop based subgraph/subtree analysis algorithm, and performs significantly better than prior approaches for very large graphs and templates. Another unique aspect is that SAHAD is also amenable to running quite easily on Amazon EC2, without needs for any system level optimization.

Efficient distributed approximation algorithms via probabilistic tree embeddings

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 use the embedding to obtain expected O(log n)-approximate distributed algorithms for the generalized Steiner forest problem, the minimum routing cost spanning tree problem, and the

A Study of Information Diffusion over a Realistic Social Network Model

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Subgraph Enumeration in Large Social Contact Networks Using Parallel Color Coding and Streaming

-source shortest paths problem in arbitrary networks. The time complexities of our algorithms are within a polylogarithmic factor of the optimum. The distributed construction of the FRT embedding is based on the computation of least elements (LE) lists, a distributed data structure that might be of independent interest. Assuming a global order on the nodes of a network, the LE list of a node stores the smallest node (w.r.t. the given order) within every distance

Edge-to-edge measurement-based distributed network monitoring

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