V. S. Anil Kumar

Modelling disease outbreaks in realistic urban social networks

Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

Cellular traffic offloading through opportunistic communications: a case study

Due to the increasing popularity of various applications for smartphones, 3G networks are currently overloaded by mobile data traffic. Offloading cellular traffic through opportunistic communications is a promising solution to partially solve this problem, because there is no monetary cost for it. As a case study, we investigate the target-set selection problem for information delivery in the emerging Mobile Social Networks (MoSoNets). We propose to exploit opportunistic communications to facilitate the information dissemination and thus reduce the amount of cellular traffic. In particular, we study how to select the target set with only k users, such that we can minimize the cellular data traffic. In this scenario, initially the content service providers deliver information over cellular networks to only users in the target set. Then through opportunistic communications, target-users will further propagate the information among all the subscribed users. Finally, service providers will send the information to users who fail to receive it before the delivery deadline (i.e., delay-tolerance threshold). We propose three algorithms, called Greedy, Heuristic, and Random, for this problem and evaluate their performance through an extensive trace-driven simulation study. The simulation results verify the efficiency of these algorithms for both synthetic and real-world mobility traces. For example, the Heuristic algorithm can offload cellular traffic by up to 73.66% for a real-world mobility trace.

EpiFast: a fast algorithm for large scale realistic epidemic simulations on distributed memory systems

Large scale realistic epidemic simulations have recently become an increasingly important application of high-performance computing. We propose a parallel algorithm, EpiFast, based on a novel interpretation of the stochastic disease propagation in a contact network. We implement it using a master-slave computation model which allows scalability on distributed memory systems. EpiFast runs extremely fast for realistic simulations that involve: (i) large populations consisting of millions of individuals and their heterogeneous details, (ii) dynamic interactions between the disease propagation, the individual behaviors, and the exogenous interventions, as well as (iii) large number of replicated runs necessary for statistically sound estimates about the stochastic epidemic evolution. We find that EpiFast runs several magnitude faster than another comparable simulation tool while delivering similar results. EpiFast has been tested on commodity clusters as well as SGI shared memory machines. For a fixed experiment, if given more computing resources, it scales automatically and runs faster. Finally, EpiFast has been used as the major simulation engine in real studies with rather sophisticated settings to evaluate various dynamic interventions and to provide decision support for public health policy makers.

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.

Cross-layer latency minimization in wireless networks with SINR constraints

Recently, there has been substantial interest in the design of cross-layer protocols for wireless networks. These protocols optimize certain performance metric(s) of interest (e.g. latency, energy, rate) by jointly optimizing the performance of multiple layers of the protocol stack. Algorithm designers often use geometric-graph-theoretic models for radio interference to design such cross-layer protocols. In this paper we study the problem of designing cross-layer protocols for multi-hop wireless networks using a more realistic Signal to Interference plus Noise Ratio (SINR) model for radio interference. The following cross-layer latency minimization problem is studied: Given a set V of transceivers, and a set of source-destination pairs, (i) choose power levels for all the transceivers, (ii) choose routes for all connections, and (iii) construct an end-to-end schedule such that the SINR constraints are satisfied at each time step so as to minimize the make-span of the schedule (the time by which all packets have reached their respective destinations). We present a polynomial-time algorithm with provable worst-case performance guarantee for this cross-layer latency minimization problem. As corollaries of the algorithmic technique we show that a number of variants of the cross-layer latency minimization problem can also be approximated efficiently in polynomial time. Our work extends the results of Kumar et al. (Proc. SODA, 2004) and Moscibroda et al. (Proc. MOBIHOC, 2006). Although our algorithm considers multiple layers of the protocol stack, it can naturally be viewed as compositions of tasks specific to each layer --- this allows us to improve the overall performance while preserving the modularity of the layered structure.

Multi-channel scheduling algorithms for fast aggregated convergecast in sensor networks

Fast and periodic collection of aggregated data is of considerable interest for mission-critical and continuous monitoring applications in sensor networks. In the many-to-one communication paradigm known as convergecast, we consider scenarios where data packets are aggregated at each hop en route to a sink node along a tree-based routing topology and focus on maximizing the data collection rate at the sink by employing TDMA scheduling and multiple frequency channels. Our key result in the paper lies in proving that minimizing the schedule length for an arbitrary network in the presence of multiple frequencies is NP-hard, and in designing approximation algorithms with worst-case provable performance guarantees for geometric networks. In particular, we design a constant factor approximation for networks modeled as unit disk graphs (UDG) where every node has a uniform transmission range, and a O(Δ(T)log n) approximation for general disk graphs where nodes have different transmission ranges; n is the number of nodes in the network and Δ(T) is the maximum node degree on a given routing tree T. We also prove that a constant factor approximation is achievable on UDG even for unknown routing topologies so long as the maximum node degree in the tree is bounded by a constant. We also show that finding the minimum number of frequencies required to remove all the interfering links in an arbitrary network in NP-hard. We give an upper bound on the maximum number of such frequencies required and propose a polynomial time algorithm that minimizes the schedule length under this scenario. Finally, we evaluate our algorithms through simulations and show various trends in performance for different network parameters.

Equilibria in topology control games for ad hoc networks

We study topology control problems in ad hoc networks, where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maximize their own utility that they get out of the network without considering the overall performance of the network. Game theory is the appropriate tool to study such selfish nodes: we define several topology control games in which the nodes need to choose power levels in order to connect to other nodes in the network to reach their communication partners while at the same time minimizing their costs. We study Nash equilibria and show that -- among the games we define -- these can only be guaranteed to exist if all network nodes are required to be connected to all other nodes (we call this the Strong Connectivity Game). We give asymptotically tight bounds for the worst case quality of a Nash equilibrium in the Strong Connectivity Game and we improve these bounds for randomly distributed nodes. We then study the computational complexity of finding Nash equilibria and show that a polynomial-time algorithm finds Nash equilibria whose costs are at most a factor 2 off the minimum cost possible; for a variation called Connectivity Game, where each node is only required to be connected (possibly via intermediate nodes) to a given set of nodes, we show that answering the question, if a Nash equilibrium exists, is NP-hard, if the network graph satisfies the triangle inequality. For a second game called Reachability Game, where each node tries to reach as many other nodes as possible, while minimizing its radius, we show that 1+o(1)-approximate Nash equilibria exist for randomly distributed nodes. Our work is a first step towards game-theoretic analyses of ad hoc networks.

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.

Improved Results for Stackelberg Scheduling Strategies

We continue the study initiated in [13] on Stackelberg Scheduling Strategies. We are given a set of m independent parallel machines or equivalently a set of m parallel edges, each with a load dependent latency function. The setting is that of a non-cooperative game: players route their flow so as minimize their individual latencies. Additionally, there is a single player (the leader), who controls an a fraction of the total flow. The goal is to find a strategy for the leader (i.e. an assignment of flow to individual links) such that the selfish users react so as to minimize the total latency of the system. Building on the recent results in [13,14], we devise a fully polynomial approximate Stackelberg scheme that runs in time poly(m, 1/?) and results in an assignment whose cost is within a (1 + ?) factor of the optimum Stackelberg strategy. We also study the generalization to multiple rounds. It is easy to see that more than two rounds do not help. We show that the two round Stackelberg strategy (denoted 2SS) always dominates the one round scheme. We also consider extensions of the above results to special graphs, and special kind of latency functions.