Low Complexity Sequential Search with Size-Dependent Measurement Noise

TL;DR

This paper introduces two low-complexity, connected-region search strategies, dyaPM and hiePM, for target localization under size-dependent measurement noise, achieving asymptotic optimality and practical efficiency.

Contribution

The paper proposes two novel search algorithms, dyaPM and hiePM, with low computational complexity and hierarchical structure, tailored for size-dependent noise scenarios.

Findings

dyaPM is asymptotically optimal in search time complexity.

hiePM is near-optimal in rate and has reduced query set cardinality.

Both methods outperform prior approaches in non-asymptotic regimes.

Abstract

This paper considers a target localization problem where at any given time an agent can choose a region to query for the presence of the target in that region. The measurement noise is assumed to be increasing with the size of the query region the agent chooses. Motivated by practical applications such as initial beam alignment in array processing, heavy hitter detection in networking, and visual search in robotics, we consider practically important complexity constraints/metrics: \textit{time complexity}, \textit{computational and memory complexity}, and the complexity of possible query sets in terms of geometry and cardinality. Two novel search strategy, $dyaPM$ and $hiePM$, are proposed. Pertinent to the practicality of out solutions, $dyaPM$ and $hiePM$ are of a connected query geometry (i.e. query set is always a connected set) implemented with low computational and memory complexity. Additionally, $hiePM$ has a hierarchical structure and, hence, a further reduction in the cardinality of possible query sets, making $hiePM$ practically suitable for applications such as beamforming in array processing where memory limitations favors a smaller codebook size. Through a unified analysis with Extrinsic Jensen Shannon (EJS) Divergence, $dyaPM$ is shown to be asymptotically optimal in search time complexity (asymptotic in both resolution (rate) and error (reliability)). On the other hand, $hiePM$ is shown to be near-optimal in rate. In addition, both $hiePM$ and $dyaPM$ are shown to outperform prior work in the non-asymptotic regime.