Minimizing the Weighted Number of Tardy Jobs via (max,+)-Convolutions
研究单机调度中最小化加权延迟作业数量的经典问题，提出一个简单的伪多项式时间算法，在某些场景下优于Lawler和Moore算法，并给出基于SETH的下界。
In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60’s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH). History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported by the Israel Science Foundation [Grant 1070/20].