Subhashini Krishnasamy

The behavior of epidemics under bounded susceptibility

We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint is motivated by modern social networks, wherein messages are broadcast to all neighbors, but attention spans are limited. Bounded susceptibility also arises in distributed computing applications with download bandwidth constraints, and in human epidemics under quarantine policies. Network epidemics have been extensively studied in literature; prior work characterizes the graph structures required to ensure fast spreading under the SI dynamics, and long lifetime under the SIS dynamics. In particular, these conditions turn out to be meaningful for two classes of networks of practical relevance -- dense, uniform (i.e., clique-like) graphs, and sparse, structured (i.e., star-like) graphs. We show that bounded susceptibility has a surprising impact on epidemic behavior in these graph families. For the SI dynamics, bounded susceptibility has no effect on star-like networks, but dramatically alters the spreading time in clique-like networks. In contrast, for the SIS dynamics, clique-like networks are unaffected, but star-like networks exhibit a sharp change in extinction times under bounded susceptibility. Our findings are useful for the design of disease-resistant networks and infrastructure networks. More generally, they show that results for existing epidemic models are sensitive to modeling assumptions in non-intuitive ways, and suggest caution in directly using these as guidelines for real systems.

Scheduling in densified networks: Algorithms and performance

With increasing data demand, wireless networks are evolving to a hierarchical architecture where coverage is provided by both wide-area base-stations (BS) and dense deployments of short-range access nodes (AN) (e.g., small cells). The dense scale and mobility of users provide new challenges for scheduling: (i) High flux in mobile-to-AN associations, where mobile nodes quickly change associations with access nodes (time-scale of seconds) due to their small footprint, and (ii) multi-point connectivity, where mobile nodes are simultaneously connected to several access nodes at any time. We study such a densified scenario with multi-channel wireless links (e.g., multi-channel OFDM) between nodes (BS/AN/mobile). We first show that traditional algorithms that forward each packet at most once, either to a single access node or a mobile user, do not have good delay performance. We argue that the fast association dynamics between access nodes and mobile users necessitate a multi-point relaying strategy, where multiple access nodes have duplicate copies of the data, and coordinate to deliver data to the mobile user. Surprisingly, despite data replication and no coordination between ANs, we show that our algorithm (a distributed scheduler — DIST) can approximately stabilize the system in large-scale instantiations of this setting, and further, performs well from a queue-length/delay perspective (shown via large deviation bounds).

Spectrum sharing and scheduling in D2D-enabled dense cellular networks

We study device-to-device (D2D) enabled hierarchical cellular networks consisting of a macro base station (BS), a dense network of access nodes (ANs) and mobile users, where spectrum is shared between cellular traffic and D2D traffic. Further, (the receivers of) mobile users dynamically time-share between the cellular and D2D networks. We develop algorithms for channel allocation and mobile-user receiver mode selection (choosing which network to participate in) with the objectives of minimizing delay for cellular traffic, and capacity maximization for D2D traffic. Our proposed solution takes advantage of the unique features offered by large and densified cellular networks such as multi-point connectivity, channel diversity, spatial reuse and load distribution. Given a BS-to-mobile delay requirement of d + 1 time-slots, we show that by appropriately scheduling channels and receiver modes, we can (with exponentially high probability) guarantee that cellular traffic reaches its intended destination within d timeslots. By leveraging spatial channel reuse, we show that this is achieved by utilizing a vanishingly small fraction of the available spatial capacity. Further, in the presence of delay-constrained cellular traffic, our scheduling algorithm guarantees D2D traffic can achieve rates within a (1-1/d) factor of the corresponding achievable rates without cellular traffic.

Augmenting max-weight with explicit learning for wireless scheduling with switching costs

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to opportunistically switch off a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach — a Max-Weight algorithm along with a Lyapunov-based stability argument — does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

Detecting Sponsored Recommendations

Personalized recommender systems provide great opportunities for targeted advertisements, by displaying ads alongside genuine recommendations. We consider a biased recommendation system where such ads are displayed without any tags (disguised as genuine recommendations), rendering them indistinguishable to users. We consider the problem of detecting such a bias and propose an algorithm that uses statistical analysis based on binary feedback data from a subset of users. We prove that the proposed algorithm detects bias with high probability for a broad class of recommendation systems with sufficient number of feedback samples.

On the scaling of interference alignment under delay and power constraints

Future wireless standards such as 5G envision dense wireless networks with large number of simultaneously connected devices. In this context, interference management becomes critical in achieving high spectral efficiency. Orthogonal signaling, which limits the number of users utilizing the resource simultaneously, gives a sum-rate that remains constant with increasing number of users. An alternative approach called interference alignment promises a throughput that scales linearly with the number of users. However, this approach requires very high SNR or long time duration for sufficient channel variation, and therefore may not be feasible in real wireless systems. We explore ways to manage interference in large networks with delay and power constraints. Specifically, we devise an interference phase alignment strategy that combines precoding and scheduling without using power control to exploit the diversity inherent in a system with large number of users. We show that this scheme achieves a sum-rate that scales almost logarithmically with the number of users. We also show upper bounds on the sum-rate within the restricted class of single-symbol phase alignment schemes. Specifically, we prove that no scheme in this class can achieve better than logarithmic scaling of the sum-rate.