In many networks the operator is faced with nodes that report a potentially important phenomenon such as failures, illnesses, and viruses. The operator is faced with the question: Is it spreading over the network, or simply occurring at random? We seek to answer this question from highly noisy and incomplete data, where at a single point in time we are given a possibly very noisy subset of the infected population (including false positives and negatives). While previous work has focused on uniform spreading rates for the infection, heterogeneous graphs with unequal edge weights are more faithful models of reality. Critically, the network structure may not be fully known and modeling epidemic spread on unknown graphs relies on non-homogeneous edge (spreading) weights. Such heterogeneous graphs pose considerable challenges, requiring both algorithmic and analytical development. We develop an algorithm that can distinguish between a spreading phenomenon and a randomly occurring phenomenon while using only local information and not knowing the complete network topology and the weights. Further, we show that this algorithm can succeed even in the presence of noise, false positives and unknown graph edges.

We consider the problem of detecting an epidemic in a population where individual diagnoses are extremely noisy. We show that exclusively local, approximate knowledge of the contact network suffices to accurately detect the epidemic. The motivation for this problem is the plethora of examples (influenza strains in humans, or computer viruses in smartphones, etc.) where reliable diagnoses are scarce, but noisy data plentiful. In flu or phone-viruses, exceedingly few infected people/phones are professionally diagnosed (only a small fraction go to a doctor) but less reliable secondary signatures (e.g., people staying home, or greater-than-typical upload activity) are more readily available.

The history of infections and epidemics holds famous examples where understanding, containing, and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV, and most computer viruses spread person to person, device to device, and through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper, we study two fundamental questions of detection. First, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a random illness operating independently of any contact network (e.g., seasonal allergies)? Second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread-the causative network-without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions that networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the d-dimensional grid, and the Erdös-Renyi graphs.

From Cholera, AIDS/HIV, and Malaria, to rumors and viral video, understanding the causative network behind an epidemic's spread has repeatedly proven critical for managing the spread (controlling or encouraging, as the case may be). Our current approaches to understand and predict epidemics rely on the scarce, but exact/reliable, expert diagnoses. This paper proposes a different way forward: use more readily available but also more noisy data with {\em many false negatives and false positives}, to determine the causative network of an epidemic. Specifically, we consider an epidemic that spreads according to one of two networks. At some point in time we see a small random subsample (perhaps a vanishingly small fraction) of those infected, along with an order-wise similar number of false positives. We derive sufficient conditions for this problem to be detectable, and provide an efficient algorithm that solves the hypothesis testing problem. We apply this model to two settings. In the first setting, we simply want to distinguish between random illness (a complete graph) and an epidemic (spread along a structured graph). In the second, we have a superposition of both of these, and we wish to detect which is the strongest component.

Computer (and human) networks have long had to contend with spreading viruses. Effectively controlling or curbing an outbreak requires understanding the dynamics of the spread. A virus that spreads by taking advantage of physical links or user-acquaintance links on a social network can grow explosively if it spreads beyond a critical radius. On the other hand, random infections (that do not take advantage of network structure) have very different propagation characteristics. If too many machines (or humans) are infected, network structure becomes essentially irrelevant, and the different spreading modes appear identical. When can we distinguish between mechanics of infection? Further, how can this be done efficiently? This paper studies these two questions. We provide sufficient conditions for different graph topologies, for when it is possible to distinguish between a random model of infection and a spreading epidemic model, with probability of misclassification going to zero. We further provide efficient algorithms that are guaranteed to work in different regimes.

Routing to mobile nodes in a wireless network is conventionally performed by associating a static IP address (or a geographic location) to each node, and routing to that address using routing tables at intermediate nodes that are updated periodically to reflect mobility-induced network topology changes. This mode of routing works when the mobiles' speeds as well as the number of mobiles are small. However, in the presence of large number of fast-moving mobiles, such approaches are infeasible and can lead to excessive overheads, routing failures and hence, throughput loss. In this paper, we consider a wireless network over a domain with a collection of static nodes (that form a connected cover of the domain) and mobile nodes, where the mobile nodes can move in an arbitrary (non-ergodic) manner over sub-domains of the network. For such a system, we develop new routing algorithms (based on a spatial multi-resolution search) that we show are efficient both in terms of routing overheads and throughput. In particular, we show that the achievable rate region of the proposed algorithm is within a poly-logarithmic constant of the optimal rate region with non-ergodic mobility.