Abstract:
This thesis explores the dynamics of online algorithms, with a focus on the List Update Problem in online optimization. Our study revolves around the analysis of various algorithmic strategies, under the frameworks of online algorithms, competitive ratios, and the potential function method. A pivotal aspect is the examination of the Per Request Prediction model, where each element request is accompanied by information about its subsequent request, thereby augmenting the decision-making in these algorithms. We construct an optimal offline algorithm and analyze its performance in comparison to online algorithms. Our research encompasses the competitive analysis of both deterministic and randomized cases of the List Update Problem, considering scenarios with and without predictive models. We delve into the concepts of consistency and robustness in predictive online algorithms and investigate the influence of lookahead models on algorithmic efficacy. Future work is directed towards developing an adversary for the problem statement, inspired by adversarial construction methodologies in the literature. This approach will facilitate an evaluation of the Per Request Prediction model’s impact on the lower bound competitive ratio in online algorithms.
