Amitabha Bagchi

Spatio-temporal and events based analysis of topic popularity in twitter

We present the first comprehensive characterization of the diffusion of ideas on Twitter, studying more than 5.96 million topics that include both popular and less popular topics. On a data set containing approximately 10 million users and a comprehensive scraping of 196 million tweets, we perform a rigorous temporal and spatial analysis, investigating the time-evolving properties of the subgraphs formed by the users discussing each topic. We focus on two different notions of the spatial: the network topology formed by follower-following links on Twitter, and the geospatial location of the users. We investigate the effect of initiators on the popularity of topics and find that users with a high number of followers have a strong impact on topic popularity. We deduce that topics become popular when disjoint clusters of users discussing them begin to merge and form one giant component that grows to cover a significant fraction of the network. Our geospatial analysis shows that highly popular topics are those that cross regional boundaries aggressively.

Deterministic sampling and range counting in geometric data streams

We present memory-efficient deterministic algorithms for constructing ∈-nets and ∈-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.

The Effect of Faults on Network Expansion

We study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain and still contain a large (i.e., linear-sized) connected component with approximately the same expansion as the original fault-free network. We use a pruning technique that culls away those parts of the faulty network that have poor expansion. The faults may occur at random or be caused by an adversary. Our techniques apply in either case. In the adversarial setting we prove that for every network with expansion

Seller-Focused Algorithms for Online Auctioning

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Constructing Disjoint Paths for Secure Communication

a large connected component with basically the same expansion as the original network exists for up to a constant times

Towards the use of online social networks for efficient Internet content distribution

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Short length Menger's theorem and reliable optical routing

faults. We show this result is tight in the sense that every graph G of size n and uniform expansion

Towards characterization of actor evolution and interactions in news corpora

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Algorithms for Fault-Tolerant Routing in Circuit-Switched Networks

can be broken into components of size o(n) with

Algorithms for fault-tolerant routing in circuit switched networks

\omega(\alpha(n) \cdot n)