Learning-Augmented and Randomized Algorithms for Line Aggregation with Delays

• URL: http://arxiv.org/abs/2607.27807v1
• Date: Thu, 30 Jul 2026 07:47:07 GMT
• Title: Learning-Augmented and Randomized Algorithms for Line Aggregation with Delays
• Abstract summary: We study learning-augmented and randomized online aggregation with delays on a line metric.<n>For each $in (0,1]$, we first propose a deterministic learning-augmented textscBalance algorithm that is $(4/+1/2)$-robust.<n>We also propose a randomized algorithm for the problem in the classical adversarial model, which is $(e+1)$-competitive against an oblivious adversary.
• Score: 7.216833894546792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies learning-augmented and randomized online aggregation with delays on a line metric. We consider advice given as online suggested service lengths, and evaluate the algorithms in terms of robustness and consistency. For each $λ\in (0,1]$, we first propose a deterministic learning-augmented \textsc{Balance} algorithm that is $(4/λ+1/λ^2)$-robust and $(4+λ)$-consistent. We also propose a randomized algorithm for the problem in the classical adversarial model, which is $(e+1)$-competitive against an oblivious adversary, improving over the deterministic $5$-competitive \textsc{Balance} benchmark~\cite{bienkowski2013chain}. Notably, this competitive ratio is even lower than the lower bound of $4$ for deterministic online algorithms. Moreover, we establish a lower bound of $e$ on the competitive ratio of randomized online algorithms, improving the previous lower bound of $e/(e-1)$. Besides, we combine the two ideas and obtain a randomized learning-augmented algorithm that is $(e/λ+1/λ^2)$-robust and $(e+λ)$-consistent. Finally, we conduct numerical experiments to complement our theoretical analysis and evaluate the empirical performance of our algorithms.

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