Greedy algorithms are among the most elementary ones in theoretical computer science and understanding the conditions under which they yield an optimum solution is a widely studied problem. Greedoids were introduced by Korte and Lovász at the beginning of the 1980s as a generalization of matroids. One of the basic motivations of the notion was to extend the theoretical background behind greedy algorithms beyond the well-known results on matroids. Indeed, many well-known algorithms of a greedy nature that cannot be interpreted in a matroid-theoretical context are special cases of the greedy algorithm on greedoids. Although this algorithm turns out to be optimal in surprisingly many cases, no general theorem is known that explains this phenomenon in all these cases. Furthermore, certain claims regarding this question that were made in the original works of Korte and Lovász turned out to be false only most recently. The aim of this paper is to revisit and straighten out this question: we summarize recent progress and we also prove new results in this field. In particular, we generalize a result of Korte and Lovász and thus we obtain a sufficient condition for the optimality of the greedy algorithm that covers a much wider range of known applications than the original one.

贪婪算法是理论计算机科学中最基本的算法之一，了解它们产生最佳解决方案的条件是一个广泛研究的问题。1980 年代初期，Korte 和 Lovász 引入了 Greedoids 作为拟阵的推广。该概念的基本动机之一是将贪婪算法背后的理论背景扩展到拟阵的众所周知的结果之外。事实上，许多众所周知的无法在拟阵理论背景下解释的贪婪算法是贪婪算法的特例。尽管该算法在很多情况下都证明是最优的，但在所有这些情况下，没有已知的一般定理可以解释这种现象。此外，在 Korte 和 Lovász 的原著中提出的关于这个问题的某些说法直到最近才被证明是错误的。本文的目的是重新审视和理顺这个问题：我们总结了最近的进展，并证明了该领域的新成果。特别是，我们概括了 Korte 和 Lovász 的结果，因此我们获得了贪心算法最优性的充分条件，该算法涵盖了比原始算法更广泛的已知应用程序。