The knowledge of future partial information in the form of a lookahead to design efficient online algorithms is a theoretically-efficient and realistic approach to solving computational problems. Design and analysis of semi-online algorithms with extra-piece-of-information (EPI) as a new input parameter has gained the attention of the theoretical computer science community in the last couple of decades. Though competitive analysis is a pessimistic worst-case performance measure to analyze online algorithms, it has immense theoretical value in developing the foundation and advancing the state-of-the-art contributions in online and semi-online scheduling. In this paper, we study and explore the impact of lookahead as an EPI in the context of online scheduling in identical machine frameworks. We introduce a $k$-lookahead model and design improved competitive semi-online algorithms. For a $2$-identical machine setting, we prove a lower bound of $\frac{4}{3}$ and design an optimal algorithm with a matching upper bound of $\frac{4}{3}$ on the competitive ratio. For a $3$-identical machine setting, we show a lower bound of $\frac{15}{11}$ and design a $\frac{16}{11}$-competitive improved semi-online algorithm.

翻译：以未来部分信息（即前瞻）形式的知识来设计高效在线算法，是解决计算问题的一种理论高效且现实的方法。在过去几十年中，将额外信息片段作为新输入参数来设计与分析半在线算法，已引起理论计算机科学界的关注。尽管竞争分析是分析在线算法的悲观最坏情况性能度量，但在发展在线与半在线调度基础理论及推进前沿成果方面具有重要理论价值。本文在相同机器框架下，研究并探讨了前瞻作为额外信息片段对在线调度的影响。我们引入了$k$-前瞻模型，并设计了改进的竞争性半在线算法。对于2台相同机器情形，我们证明了竞争比的下界为$\frac{4}{3}$，并设计了匹配上界$\frac{4}{3}$的最优算法。对于3台相同机器情形，我们给出了$\frac{15}{11}$的下界，并设计了竞争比为$\frac{16}{11}$的改进型半在线算法。