带截止期多层集结问题的$D$ -竞争算法
A $D$-competitive algorithm for the Multilevel Aggregation Problem with Deadlines
摘要：
在本文中，我们考虑了Bienkowski et al.（2015），Buchbinder et al.（2017）以及Azar and Touitou（2019）先前研究的具有截止日期的多级聚合问题（MLAPD）。这是一个在线问题，其中算法服务随着时间的推移到达的请求，并且可以通过聚合类似的请求来节省成本。成本以有根树的形式构成。这个问题有许多重要的应用领域，如多播，传感器网络和供应链管理。特别地，TCP确认问题、联合补给问题和装配问题都是延迟问题的特殊情况。我们提出了一个$D$ -竞争算法的MLAPD。这击败了Buchbinder等人（2017）给出的$6(D+1)$竞争算法。我们的方法阐明了问题的关键结构方面，并提供了一个算法，比以前的方法更简单的实现。我们还针对问题的特殊情况给出了改进的竞争比。
英文摘要：
In this paper, we consider the multi-level aggregation problem with deadlines (MLAPD) previously studied by Bienkowski et al. (2015), Buchbinder et al. (2017), and Azar and Touitou (2019). This is an online problem where the algorithm services requests arriving over time and can save costs by aggregating similar requests. Costs are structured in the form of a rooted tree. This problem has applications to many important areas such as multicasting, sensor networks, and supply-chain management. In particular, the TCP-acknowledgment problem, joint-replenishment problem, and assembly problem are all special cases of the delay version of the problem. We present a $D$-competitive algorithm for MLAPD. This beats the $6(D+1)$-competitive algorithm given in Buchbinder et al. (2017). Our approach illuminates key structural aspects of the problem and provides an algorithm that is simpler to implement than previous approaches. We also give improved competitive ratios for special cases of the problem.
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