arXiv subjects

Amitabha Bagchi

Publications and source records attributed to Amitabha Bagchi.

26 records · Page 2Linked to original sources

arXiv2012

Topic Diffusion and Emergence of Virality in Social Networks

We propose a stochastic model for the diffusion of topics entering a social network modeled by a Watts-Strogatz graph. Our model sets into play an implicit competition between these topics as they vie for the attention of users in the network. The dynamics of our model are based on notions taken from real-world OSNs like Twitter where users either adopt an exogenous topic or copy topics from their neighbors leading to endogenous propagation. When instantiated correctly, the model achieves a viral regime where a few topics garner unusually good response from the network, closely mimicking the behavior of real-world OSNs. Our main contribution is our description of how clusters of proximate users that have spoken on the topic merge to form a large giant component making a topic go viral. This demonstrates that it is not weak ties but actually strong ties that play a major part in virality. We further validate our model and our hypotheses about its behavior by comparing our simulation results with the results of a measurement study conducted on real data taken from Twitter.

cs.SI↗

arXiv2011

Spatio-Temporal Analysis of Topic Popularity in Twitter

We present the first comprehensive characterization of the diffusion of ideas on Twitter, studying more than 4000 topics that include both popular and less popular topics. On a data set containing approximately 10 million users and a comprehensive scraping of all the tweets posted by these users between June 2009 and August 2009 (approximately 200 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 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.

cs.SI↗

arXiv2010

Relating Web pages to enable information-gathering tasks

We argue that relationships between Web pages are functions of the user's intent. We identify a class of Web tasks - information-gathering - that can be facilitated by a search engine that provides links to pages which are related to the page the user is currently viewing. We define three kinds of intentional relationships that correspond to whether the user is a) seeking sources of information, b) reading pages which provide information, or c) surfing through pages as part of an extended information-gathering process. We show that these three relationships can be productively mined using a combination of textual and link information and provide three scoring mechanisms that correspond to them: {\em SeekRel}, {\em FactRel} and {\em SurfRel}. These scoring mechanisms incorporate both textual and link information. We build a set of capacitated subnetworks - each corresponding to a particular keyword - that mirror the interconnection structure of the World Wide Web. The scores are computed by computing flows on these subnetworks. The capacities of the links are derived from the {\em hub} and {\em authority} values of the nodes they connect, following the work of Kleinberg (1998) on assigning authority to pages in hyperlinked environments. We evaluated our scoring mechanism by running experiments on four data sets taken from the Web. We present user evaluations of the relevance of the top results returned by our scoring mechanisms and compare those to the top results returned by Google's Similar Pages feature, and the {\em Companion} algorithm proposed by Dean and Henzinger (1999).

cs.IR↗

arXiv2009

Hierarchical neighbor graphs: A low stretch connected structure for points in Euclidean space

We introduce hierarchical neighbor graphs, a new architecture for connecting ad hoc wireless nodes distributed in a plane. The structure has the flavor of hierarchical clustering and requires only local knowledge and minimal computation at each node to be formed and repaired. Hence, it is a suitable interconnection model for an ad hoc wireless sensor network. The structure is able to use energy efficiently by reorganizing dynamically when the battery power of heavily utilized nodes degrades and is able to achieve throughput, energy efficiency and network lifetimes that compare favorably with the leading proposals for data collation in sensor networks such as LEACH (Heinzelman et. al., 2002). Additionally, hierarchical neighbor graphs have low power stretch i.e. the power required to connect nodes through the network is a small factor higher than the power required to connect them directly. Our structure also compares favorably to mathematical structures proposed for connecting points in a plane e.g. nearest-neighbor graphs (Ballister et. al., 2005), $θ$-graphs (Ruppert and Seidel, 1991), in that it has expected constant degree and does not require any significant computation or global information to be formed.

cs.NI↗

arXiv2008

On the metric distortion of nearest-neighbour graphs on random point sets

We study the graph constructed on a Poisson point process in $d$ dimensions by connecting each point to the $k$ points nearest to it. This graph a.s. has an infinite cluster if $k > k_c(d)$ where $k_c(d)$, known as the critical value, depends only on the dimension $d$. This paper presents an improved upper bound of 188 on the value of $k_c(2)$. We also show that if $k \geq 188$ the infinite cluster of $\NN(2,k)$ has an infinite subset of points with the property that the distance along the edges of the graphs between these points is at most a constant multiplicative factor larger than their Euclidean distance. Finally we discuss in detail the relevance of our results to the study of multi-hop wireless sensor networks.

cs.NI↗

arXiv2008

Sparse power-efficient topologies for wireless ad hoc sensor networks

We study the problem of power-efficient routing for multihop wireless ad hoc sensor networks. The guiding insight of our work is that unlike an ad hoc wireless network, a wireless ad hoc sensor network does not require full connectivity among the nodes. As long as the sensing region is well covered by connected nodes, the network can perform its task. We consider two kinds of geometric random graphs as base interconnection structures: unit disk graphs $\UDG(2,λ)$ and $k$-nearest-neighbor graphs $\NN(2,k)$ built on points generated by a Poisson point process of density $λ$ in $\RR^2$. We provide subgraph constructions for these two models $\US(2,λ)$ and $\NS(2,k)$ and show that there are values $λ_s$ and $k_s$ above which these constructions have the following good properties: (i) they are sparse; (ii) they are power-efficient in the sense that the graph distance is no more than a constant times the Euclidean distance between any pair of points; (iii) they cover the space well; (iv) the subgraphs can be set up easily using local information at each node. We also describe a simple local algorithm for routing packets on these subgraphs. Our constructions also give new upper bounds for the critical values of the parameters $λ$ and $k$ for the models $\UDG(2,λ)$ and $\NN(2,k)$.

cs.NI↗

arXiv2004

The Effect of Faults on Network Expansion

In this paper 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 so that it still contains a large (i.e. linear-sized) connected component that still has approximately the same expansion as the original fault-free network. For this we apply a pruning technique which culls away parts of the faulty network which have poor expansion. This technique can be applied to both adversarial faults and to random faults. For adversarial faults we prove that for every network with expansion alpha, a large connected component with basically the same expansion as the original network exists for up to a constant times alpha n faults. This result is tight in the sense that every graph G of size n and uniform expansion alpha(.), i.e. G has an expansion of alpha(n) and every subgraph G' of size m of G has an expansion of O(alpha(m)), can be broken into sublinear components with omega(alpha(n) n) faults. For random faults we observe that the situation is significantly different, because in this case the expansion of a graph only gives a very weak bound on its resilience to random faults. More specifically, there are networks of uniform expansion O(sqrt{n}) that are resilient against a constant fault probability but there are also networks of uniform expansion Omega(1/log n) that are not resilient against a O(1/log n) fault probability. Thus, a different parameter is needed. For this we introduce the span of a graph which allows us to determine the maximum fault probability in a much better way than the expansion can. We use the span to show the first known results for the effect of random faults on the expansion of d-dimensional meshes.

cs.DC↗

arXiv2003

Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-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.

cs.CG↗