arXiv subjects

Amitabha Bagchi

Publications and source records attributed to Amitabha Bagchi.

At least 19 recordsLinked to original sources

arXiv2026

Spectral Method attacks Sparse LWE, Sparse LPN and Beyond

Given a set of $k$-sparse linear equations over a ring $R$, we give algorithms to determine whether the right-hand sides are random or have a secret assignment planted with noise. For a parameter $k/2\leq l\leq n$, we give a spectral method to solve this problem in $\widetilde{O}\left(\binom{n}{l}\lvert{R}\rvert^l\right)$ time except with probability at most $n^{-\Omega(l)}$, provided the number of samples is roughly at least $\left(\frac{\lvert{R}\rvert n}{l}\right)^{k/2}$. This attack generalizes the Kikuchi method described by Wein et. al. (Journal of the ACM 2019) for $\mathbb{Z}_2$ to (commutative) rings of any finite size. We also give a simpler algorithm with better runtime than the spectral method and better sample complexity when $\lvert{R}\rvert=\omega(n/l)$. As a consequence, we obtain new sample-time tradeoffs for the decision problem of sparse LWE, sparse LPN over higher modulus $q$, and in general the distinguishing random vs planted $\mathbb{Z}_q$-linear equations for a large class of noise distributions. Our results imply a tightness of the hardness claims of Jain, Lin, Saha (Annual International Cryptology Conference, 2024) for sparse LWE.

cs.CR↗

arXiv2026

GRAPHGINI: Fostering Individual and Group Fairness in Graph Neural Networks

Graph Neural Networks (GNNs) have demonstrated impressive performance across various tasks, leading to their increased adoption in high-stakes decision-making systems. However, concerns have arisen about GNNs potentially generating unfair decisions for underprivileged groups or individuals when lacking fairness constraints. This work addresses this issue by introducing GraphGini, a novel approach that incorporates the Gini coefficient to enhance both individual and group fairness within the GNN framework. We rigorously establish that the Gini coefficient offers greater robustness and promotes equal opportunity among GNN outcomes, advantages not afforded by the prevailing Lipschitz constant methodology. Additionally, we employ the Nash social welfare program to ensure our solution yields a Pareto optimal distribution of group fairness. Extensive experimentation on real-world datasets demonstrates GraphGini's efficacy in significantly improving individual fairness compared to state-of-the-art methods while maintaining utility and group fairness.

cs.LG↗

arXiv2022

Gigs with Guarantees: Achieving Fair Wage for Food Delivery Workers

With the increasing popularity of food delivery platforms, it has become pertinent to look into the working conditions of the 'gig' workers in these platforms, especially providing them fair wages, reasonable working hours, and transparency on work availability. However, any solution to these problems must not degrade customer experience and be cost-effective to ensure that platforms are willing to adopt them. We propose WORK4FOOD, which provides income guarantees to delivery agents, while minimizing platform costs and ensuring customer satisfaction. WORK4FOOD ensures that the income guarantees are met in such a way that it does not lead to increased working hours or degrade environmental impact. To incorporate these objectives, WORK4FOOD balances supply and demand by controlling the number of agents in the system and providing dynamic payment guarantees to agents based on factors such as agent location, ratings, etc. We evaluate WORK4FOOD on a real-world dataset from a leading food delivery platform and establish its advantages over the state of the art in terms of the multi-dimensional objectives at hand.

cs.AI↗

arXiv2022

FairFoody: Bringing in Fairness in Food Delivery

Along with the rapid growth and rise to prominence of food delivery platforms, concerns have also risen about the terms of employment of the gig workers underpinning this growth. Our analysis on data derived from a real-world food delivery platform across three large cities from India show that there is significant inequality in the money delivery agents earn. In this paper, we formulate the problem of fair income distribution among agents while also ensuring timely food delivery. We establish that the problem is not only NP-hard but also inapproximable in polynomial time. We overcome this computational bottleneck through a novel matching algorithm called FairFoody. Extensive experiments over real-world food delivery datasets show FairFoody imparts up to 10 times improvement in equitable income distribution when compared to baseline strategies, while also ensuring minimal impact on customer experience.

cs.SI↗

arXiv2022

CHEX: Multiversion Replay with Ordered Checkpoints

In scientific computing and data science disciplines, it is often necessary to share application workflows and repeat results. Current tools containerize application workflows, and share the resulting container for repeating results. These tools, due to containerization, do improve sharing of results. However, they do not improve the efficiency of replay. In this paper, we present the multiversion replay problem which arises when multiple versions of an application are containerized, and each version must be replayed to repeat results. To avoid executing each version separately, we develop CHEX, which checkpoints program state and determines when it is permissible to reuse program state across versions. It does so using system call-based execution lineage. Our capability to identify common computations across versions enables us to consider optimizing replay using an in-memory cache, based on a checkpoint-restore-switch system. We show the multiversion replay problem is NP-hard, and propose efficient heuristics for it. CHEX reduces overall replay time by sharing common computations but avoids storing a large number of checkpoints. We demonstrate that CHEX maintains lightweight package sharing, and improves the total time of multiversion replay by 50% on average.

cs.DB↗

arXiv2021

FROCC: Fast Random projection-based One-Class Classification

We present Fast Random projection-based One-Class Classification (FROCC), an extremely efficient method for one-class classification. Our method is based on a simple idea of transforming the training data by projecting it onto a set of random unit vectors that are chosen uniformly and independently from the unit sphere, and bounding the regions based on separation of the data. FROCC can be naturally extended with kernels. We theoretically prove that FROCC generalizes well in the sense that it is stable and has low bias. FROCC achieves up to 3.1 percent points better ROC, with 1.2--67.8x speedup in training and test times over a range of state-of-the-art benchmarks including the SVM and the deep learning based models for the OCC task.

cs.LG↗

arXiv2020

Balance Maximization in Signed Networks via Edge Deletions

In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices can be partitioned into two subsets with negative edges present only across the partitions. Balanced portions of a graph have been shown to increase coherence among its members and lead to better performance. While existing works have focused primarily on finding the largest balanced subgraph inside a graph, we study the network design problem of maximizing balance of a target community (subgraph). In particular, given a budget $b$ and a community of interest within the signed network, we aim to make the community as close to being balanced as possible by deleting up to $b$ edges. Besides establishing NP-hardness, we also show that the problem is non-monotone and non-submodular. To overcome these computational challenges, we propose heuristics based on the spectral relation of balance with the Laplacian spectrum of the network. Since the spectral approach lacks approximation guarantees, we further design a greedy algorithm, and its randomized version, with provable bounds on the approximation quality. The bounds are derived by exploiting pseudo-submodularity of the balance maximization function. Empirical evaluation on eight real-world signed networks establishes that the proposed algorithms are effective, efficient, and scalable to graphs with millions of edges.

cs.SI↗

arXiv2020

A Distributed Laplacian Solver and its Applications to Electrical Flow and Random Spanning Tree Computation

We use queueing networks to present a new approach to solving Laplacian systems. This marks a significant departure from the existing techniques, mostly based on graph-theoretic constructions and sampling. Our distributed solver works for a large and important class of Laplacian systems that we call "one-sink" Laplacian systems. Specifically, our solver can produce solutions for systems of the form $Lx = b$ where exactly one of the coordinates of $b$ is negative. Our solver is a distributed algorithm that takes $\widetilde{O}(t_{hit} d_{\max})$ time (where $\widetilde{O}$ hides $\text{poly}\log n$ factors) to produce an approximate solution where $t_{hit}$ is the worst-case hitting time of the random walk on the graph, which is $Θ(n)$ for a large set of important graphs, and $d_{\max}$ is the generalized maximum degree of the graph. The class of one-sink Laplacians includes the important voltage computation problem and allows us to compute the effective resistance between nodes in a distributed setting. As a result, our Laplacian solver can be used to adapt the approach by Kelner and Mądry (2009) to give the first distributed algorithm to compute approximate random spanning trees efficiently.

cs.DC↗

arXiv2020

Batching and Matching for Food Delivery in Dynamic Road Networks

Given a stream of food orders and available delivery vehicles, how should orders be assigned to vehicles so that the delivery time is minimized? Several decisions have to be made: (1) assignment of orders to vehicles, (2) grouping orders into batches to cope with limited vehicle availability, and (3) adapting to dynamic positions of delivery vehicles. We show that the minimization problem is not only NP-hard but inapproximable in polynomial time. To mitigate this computational bottleneck, we develop an algorithm called FoodMatch, which maps the vehicle assignment problem to that of minimum weight perfect matching on a bipartite graph. To further reduce the quadratic construction cost of the bipartite graph, we deploy best-first search to only compute a subgraph that is highly likely to contain the minimum matching. The solution quality is further enhanced by reducing batching to a graph clustering problem and anticipating dynamic positions of vehicles through angular distance. Extensive experiments on food-delivery data from large metropolitan cities establish that FoodMatch is substantially better than baseline strategies on a number of metrics, while being efficient enough to handle real-world workloads.

cs.DB↗

arXiv2020

Lecture notes: Efficient approximation of kernel functions

These lecture notes endeavour to collect in one place the mathematical background required to understand the properties of kernels in general and the Random Fourier Features approximation of Rahimi and Recht (NIPS 2007) in particular. We briefly motivate the use of kernels in Machine Learning with the example of the support vector machine. We discuss positive definite and conditionally negative definite kernels in some detail. After a brief discussion of Hilbert spaces, including the Reproducing Kernel Hilbert Space construction, we present Mercer's theorem. We discuss the Random Fourier Features technique and then present, with proofs, scalar and matrix concentration results that help us estimate the error incurred by the technique. These notes are the transcription of 10 lectures given at IIT Delhi between January and April 2020.

cs.LG↗

arXiv2019

A Stochastic Process on a Network with Connections to Laplacian Systems of Equations

We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a queue and relay data, which is to be finally collected by a designated sink. We prove that the resulting multi-dimensional Markov chain representing the queue size of nodes has two behavior regimes depending on the value of the rate of data generation. In particular, we show that there is a non-trivial critical value of data rate below which the chain is ergodic and converges to a stationary distribution and above which it is non-ergodic, i.e., the queues at the nodes grow in an unbounded manner. We show that the rate of convergence to stationarity is geometric in the sub-critical regime. We also show the connections of this process to a class of Laplacian systems of equations whose solutions include the important problem of finding the effective resistance between two nodes, a subroutine that has been widely used to develop efficient algorithms for a number of computational problems. Hence our work provides the theoretical basis for a new class of distributed algorithms for these problems.

cs.NI↗

arXiv2019

Dynamic Partition Bloom Filters: A Bounded False Positive Solution For Dynamic Set Membership (Extended Abstract)

Dynamic Bloom filters (DBF) were proposed by Guo et. al. in 2010 to tackle the situation where the size of the set to be stored compactly is not known in advance or can change during the course of the application. We propose a novel competitor to DBF with the following important property that DBF is not able to achieve: our structure is able to maintain a bound on the false positive rate for the set membership query across all possible sizes of sets that are stored in it. The new data structure we propose is a dynamic structure that we call Dynamic Partition Bloom filter (DPBF). DPBF is based on our novel concept of a Bloom partition tree which is a tree structure with standard Bloom filters at the leaves. DPBF is superior to standard Bloom filters because it can efficiently handle a large number of unions and intersections of sets of different sizes while controlling the false positive rate. This makes DPBF the first structure to do so to the best of our knowledge. We provide theoretical bounds comparing the false positive probability of DPBF to DBF.

cs.DS↗

arXiv2018

Random walk based in-network computation of arbitrary functions

We study in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where the computed value of the function is to be consumed. We want to compute the function during the process of moving the data towards the sink. Such settings have been studied in the literature, but mainly for symmetric functions, e.g. average, parity etc., which have the specific property that the output is invariant to permutation of the operands. To the best of our knowledge, we present the first fully decentralised algorithms for arbitrary functions, which we model as those functions whose computation schema is structured as a binary tree. We propose two algorithms, Fixed Random-Compute and Flexible Random-Compute, for this problem, both of which use simple random walks on the network as their basic primitive. Assuming a stochastic model for the generation of streams of data at each source, we provide a lower and an upper bound on the rate at which Fixed Random-Compute can compute the stream of associated function values. Note that the lower bound on rate though computed for our algorithm serves as a general lower bound for the function computation problem and to the best of our knowledge is first such lower bound for asymmetric functions. We also provide upper bounds on the average time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on the network: the hitting time in the case of Fixed Random-Compute, and the mixing time in the case of Flexible Random-Compute.

cs.DC↗

arXiv2017

Learning User Representations in Online Social Networks using Temporal Dynamics of Information Diffusion

This article presents a novel approach for learning low-dimensional distributed representations of users in online social networks. Existing methods rely on the network structure formed by the social relationships among users to extract these representations. However, the network information can be obsolete, incomplete or dynamically changing. In addition, in some cases, it can be prohibitively expensive to get the network information. Therefore, we propose an alternative approach based on observations from topics being talked on in social networks. We utilise the time information of users adopting topics in order to embed them in a real-valued vector space. Through extensive experiments, we investigate the properties of the representations learned and their efficacy in preserving information about link structure among users. We also evaluate the representations in two different prediction tasks, namely, predicting most likely future adopters of a topic and predicting the geo-location of users. Experiments to validate the proposed methods are performed on a large-scale social network extracted from Twitter, consisting of about 7.7 million users and their activity on around 3.6 million topics over a month-long period.

cs.SI↗

arXiv2017

Sampling and Reconstruction Using Bloom Filters

In this paper, we address the problem of sampling from a set and reconstructing a set stored as a Bloom filter. To the best of our knowledge our work is the first to address this question. We introduce a novel hierarchical data structure called BloomSampleTree that helps us design efficient algorithms to extract an almost uniform sample from the set stored in a Bloom filter and also allows us to reconstruct the set efficiently. In the case where the hash functions used in the Bloom filter implementation are partially invertible, in the sense that it is easy to calculate the set of elements that map to a particular hash value, we propose a second, more space-efficient method called HashInvert for the reconstruction. We study the properties of these two methods both analytically as well as experimentally. We provide bounds on run times for both methods and sample quality for the BloomSampleTree based algorithm, and show through an extensive experimental evaluation that our methods are efficient and effective.

cs.DS↗

arXiv2015

On the Role of Conductance, Geography and Topology in Predicting Hashtag Virality

We focus on three aspects of the early spread of a hashtag in order to predict whether it will go viral: the network properties of the subset of users tweeting the hashtag, its geographical properties, and, most importantly, its conductance-related properties. One of our significant contributions is to discover the critical role played by the conductance based features for the successful prediction of virality. More specifically, we show that the first derivative of the conductance gives an early indication of whether the hashtag is going to go viral or not. We present a detailed experimental evaluation of the effect of our various categories of features on the virality prediction task. When compared to the baselines and the state of the art techniques proposed in the literature our feature set is able to achieve significantly better accuracy on a large dataset of 7.7 million users and all their tweets over a period of month, as well as on existing datasets.

cs.SI↗

arXiv2014

Optimal Radius for Connectivity in Duty-Cycled Wireless Sensor Networks

We investigate the condition on transmission radius needed to achieve connectivity in duty-cycled wireless sensor networks (briefly, DC-WSN). First, we settle a conjecture of Das et. al. (2012) and prove that the connectivity condition on Random Geometric Graphs (RGG), given by Gupta and Kumar (1989), can be used to derive a weak sufficient condition to achieve connectivity in DC-WSN. To find a stronger result, we define a new vertex-based random connection model which is of independent interest. Following a proof technique of Penrose (1991) we prove that when the density of the nodes approaches infinity then a finite component of size greater than 1 exists with probability 0 in this model. We use this result to obtain an optimal condition on node transmission radius which is both necessary and sufficient to achieve connectivity and is hence optimal. The optimality of such a radius is also tested via simulation for two specific duty-cycle schemes, called the contiguous and the random selection duty-cycle scheme. Finally, we design a minimum-radius duty-cycling scheme that achieves connectivity with a transmission radius arbitrarily close to the one required in Random Geometric Graphs. The overhead in this case is that we have to spend some time computing the schedule.

cs.NI↗

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↗