arXiv subjects

Raghav Mittal

Publications and source records attributed to Raghav Mittal.

4 recordsLinked to original sources

arXiv2026

HNSW with Accuracy Guarantees Using Graph Spanners

Hierarchical Navigable Small World (HNSW) graphs serve as the industry standard due to their logarithmic complexity and strong empirical performance. However, HNSW relies on greedy graph traversal, a heuristic that provides no theoretical guarantees of correctness. In this paper, we propose a novel "Certify-then-Rectify" framework that bridges the gap between the speed of heuristic search and the rigor of exact retrieval. Rather than discarding HNSW, our approach first employs a distribution-free statistical certifier to dynamically evaluate the quality of a standard HNSW search with minimal overhead. If certification indicates that the retrieved neighbors are of low quality, the framework safely escalates to a rigorous exact recovery algorithm. To make this exact recovery computationally feasible, we reinterpret the HNSW graph as a geometric spanner and utilize Extreme Value Theory to stochastically estimate its maximum empirical stretch factor. This allows us to mathematically bound the maximum distance of true nearest neighbors. Extensive evaluations on benchmark datasets demonstrate that our tiered framework delivers the average-case speed of HNSW while ensuring the worst-case correctness of exact search and outperforming other applicable approaches.

cs.DB↗

arXiv2025

Random-Access Ranked Retrieval and Similarity Search

We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over a high-dimensional feature space. This extension enables efficient solutions for a wide range of applications, from data analytics tools and database systems to recommendation systems and machine learning. We formalize the Random-Access Ranked Retrieval (RAR) problem, and extend it to Similarity Search. Our algorithmic innovations include the development of a theoretically efficient algorithm based on geometric arrangements, achieving logarithmic query time. However, this method suffers from exponential space complexity in high dimensions. Therefore, we develop a second class of algorithms based on $\varepsilon$-sampling, which consume a linear space. Since exactly locating the tuple at a specific rank is challenging due to its connection to the range counting problem, we introduce a relaxed variant called $\kappa$-Random-Access Ranked Retrieval, which returns a small subset of size $\kappa$ guaranteed to contain the target tuple. To solve this problem efficiently, we define an intermediate problem, Stripe Range Retrieval (SRR), and design a hierarchical sampling data structure tailored for narrow stripe range queries. Our method achieves practical scalability in both data size and dimensionality. We prove near-optimal bounds on the efficiency of our algorithms and validate their performance through extensive experiments on real and synthetic datasets, demonstrating scalability to millions of tuples and hundreds of dimensions.

cs.DS↗

arXiv2023

Towards Conducting Effective Locomotion Through Hardware Transformation in Head-Mounted-Device -- A Review Study

Immersiveness is the main characteristic of Virtual Reality(VR) applications. Precise integration between hardware design and software are necessary for providing a seamless virtual experience. Allowing the user to navigate the VR scene using locomotion techniques is crucial for making such experiences `immersive'. Locomotion in VR acts as a motion tracking unit for the user and simulates their movement in the virtual scene. These movements are commonly rotational, axial or translational based on the Degree-of-Freedom (DOF) of the application. To support effective locomotion, one of the primary challenges for VR practitioners is to transform their hardware from 3-DOF to 6-DOF or vice versa. We conducted a systematic review on different motion tracking methods employed in the Head-Mounted-Devices (HMD) to understand such hardware transformation. Our review discusses the fundamental aspects of the hardware-based transformation of HMDs to conduct virtual locomotion. Our observations led us to formulate a taxonomy of the tracking methods based on system design, which can eventually be used for the hardware transformation of HMDs. Our study also captures different metrics that VR practitioners use to evaluate the hardware based on the context, performance, and significance of its usage.

cs.HC↗

arXiv2021

Designing Limitless Path in Virtual Reality Environment

Walking in a Virtual Environment is a bounded task. It is challenging for a subject to navigate a large virtual environment designed in a limited physical space. External hardware support may be required to achieve such an act in a concise physical area without compromising navigation and virtual scene rendering quality. This paper proposes an algorithmic approach to let a subject navigate a limitless virtual environment within a limited physical space with no additional external hardware support apart from the regular Head-Mounted-Device (HMD) itself. As part of our work, we developed a Virtual Art Gallery as a use-case to validate our algorithm. We conducted a simple user-study to gather feedback from the participants to evaluate the ease of locomotion of the application. The results showed that our algorithm could generate limitless paths of our use-case under predefined conditions and can be extended to other use-cases.

cs.HC↗