Robotic exploration in large-scale environments is computationally demanding due to the high overhead of processing extensive frontiers. This article presents an OctoMap-based frontier exploration algorithm with predictable, asymptotically bounded performance. Unlike conventional methods whose complexity scales with environment size, our approach maintains a complexity of $\mathcal{O}(|\mathcal{F}|)$, where $|\mathcal{F}|$ is the number of frontiers. This is achieved through strategic forward and inverse sensor modeling, which enables approximate yet efficient frontier detection and maintenance. To further enhance performance, we integrate a Bayesian regressor to estimate information gain, circumventing the need to explicitly count unknown voxels when prioritizing viewpoints. Simulations show the proposed method is more computationally efficient than the existing OctoMap-based methods and achieves computational efficiency comparable to baselines that are independent of OctoMap. Specifically, the Bayesian-enhanced framework achieves up to a $54\%$ improvement in total exploration time compared to standard deterministic frontier-based baselines across varying spatial scales, while guaranteeing task completion. Real-world experiments confirm the computational bounds as well as the effectiveness of the proposed enhancement.

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