Probabilistic and Submodular Foundations for Scalable High-Dimensional Similarity Search and Distributed Optimization

Dr. Adrian Laurent Fischer

Authors

Dr. Adrian Laurent Fischer Department of Computer Science, University of Zurich, Switzerland

Keywords:

Submodular optimization, Probabilistic algorithms, Approximate nearest neighbor, Locality-sensitive

Abstract

The unprecedented growth of high-dimensional data across distributed infrastructures has intensified the need for principled algorithmic frameworks that integrate probabilistic analysis, submodular optimization, and scalable similarity search. This study develops a comprehensive theoretical synthesis that unifies probabilistic algorithmic techniques, submodular maximization strategies, approximate nearest neighbor search, multi-dimensional distributed indexing, and scalable leader coordination mechanisms. Building upon foundational probabilistic principles in algorithm design (Mitzenmacher & Upfal, 2017), classical approximation guarantees for submodular function maximization (Nemhauser & Wolsey, 1978; Nemhauser, Wolsey, & Fisher, 1978), and contemporary surveys of submodular optimization (Liu, Y., Chong, Pezeshki, & Zhang, 2020; Liu, S., 2020), this research situates submodularity as a central abstraction for resource allocation and information selection in distributed systems. Concurrently, it synthesizes hashing-based similarity search methods (Gionis, Indyk, & Motwani, 1999; Andoni & Indyk, 2006), high-dimensional indexing approaches (Houle & Sakuma, 2005; Chávez, Figueroa, & Navarro, 2008), and peer-to-peer multi-attribute routing structures (Cai et al., 2004; Ganesan, Yang, & Garcia-Molina, 2004). Through conceptual modeling and scenario-based evaluation, including application to large-scale autonomous driving datasets (Mao et al., 2021), the paper proposes an integrated probabilistic-submodular framework for distributed similarity retrieval and decision optimization. The analysis further incorporates scalable leader selection strategies for system coordination (Sayyed, 2025). The findings reveal deep theoretical connections between probabilistic concentration phenomena, greedy approximation guarantees, and locality-sensitive hashing structures, offering a unified perspective for designing efficient, resilient, and adaptive high-dimensional distributed systems. The study concludes by outlining research directions in decentralized intelligence, large-scale perception systems, and probabilistic guarantees for next-generation data infrastructures.

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