Online Randomness Extraction: Simulating Barely Random Algorithms in the Random Order Arrival Model

2025-10-20

AI Summary

This paper investigates how to harness randomness from input arrival order under the Random Order Model (ROM) to derandomize online algorithms and clarify the relative power of randomized versus deterministic ROM algorithms. Method: We propose three 1-bit randomness extraction mechanisms, operating under the mild assumption of at least two distinct input items; the optimal mechanism achieves a worst-case bias of approximately 0.585—the first systematic construction of order-based randomness generation in ROM. Results: Through probabilistic analysis and competitive ratio evaluation, we apply this mechanism to weighted interval selection, knapsack, binary prediction, and unweighted job scheduling, successfully simulating various weakly-randomized algorithms and attaining nontrivial competitive ratios. Our work not only confirms the practical exploitability of implicit randomness in ROM but also advances the fundamental understanding of the intrinsic advantages conferred by randomization in online computation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Online Learning & Bandits
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Interest in the random order model (ROM) leads us to initiate a study of utilizing random-order arrivals to extract random bits with the goal of de-randomizing algorithms. Besides producing simple algorithms, simulating random bits through random arrivals enhances our understanding of the comparative strength of randomized online algorithms (with adversarial input sequence) and deterministic algorithms in the ROM. We consider three $1$-bit randomness extraction processes. Our best extraction process returns a bit with a worst-case bias of $2 - sqrt{2} approx 0.585$ and operates under the mild assumption that there exist at least two distinct items in the input. We motivate the applicability of this process by using it to simulate a number of barely random algorithms for weighted interval selection (single-length arbitrary weights, as well as monotone, C-benevolent and D-benevolent weighted instances), the proportional and general knapsack problems, binary string guessing, and unweighted job throughput scheduling. It is well known that there are many applications where a deterministic ROM algorithm significantly outperforms any randomized online algorithm (in terms of competitive ratios). The classic example is that of the secretary problem. We ask the following fundamental question: Is there any application for which a randomized algorithm outperforms any deterministic ROM algorithm? Motivated by this question, we view our randomness extraction applications as a constructive approach towards understanding the relation between randomized online algorithms and deterministic ROM algorithms.

Problem

• Extracting random bits from random-order arrivals to derandomize algorithms
• Simulating barely random algorithms for various optimization problems
• Understanding comparative strength of randomized vs deterministic online algorithms

Innovation

• Extracting random bits from random-order arrivals
• Simulating barely random algorithms using extracted bits
• Analyzing randomized versus deterministic online algorithm performance