Median Selection with Noisy and Structural Information

Chenglin Fan, Mingyu Kang

Keywords: median selection, unreliable oracles, persistent comparison model, lazy select algorithm, partially ordered data

TL;DR: This paper studies exact median selection with unreliable oracles, proposing a hybrid algorithm with sublinear strong comparison cost under the persistent model.

Abstract:

We study the problem of computing the exact median by leveraging side information to minimize costly, exact comparisons.
We analyze this problem in two key settings:
(1) using predictions from unreliable 'weak' oracles, and
(2) exploiting known structural information in the form of a partial order. In the classical setting, we introduce a modified LazySelect algorithm that combines weak comparisons with occasional strong comparisons through majority voting. We show that this hybrid strategy has near-linear running time and can achieve high-probability correctness using only sublinear strong comparisons, even when the weak oracle is only slightly better than random guessing. Our theoretical results hold under the persistent comparison model, where resampling will not amplify the probability of correctness. In the partially ordered setting, we generalize the notion of median to directed acyclic graphs (DAGs) and show that the complexity of median selection depends heavily on the DAG's width. We complement our analysis with extensive experiments on synthetic data.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 6243