We define two algebra-based algorithms for solving the Minimum Spanning Tree problem with partially-ordered edges. The parametric structure we propose is a c-semiring, being able to represent different cost-metrics at the same time. We embed c-semirings into the Kruskal and Reverse-delete Kruskal algorithms (thus generalising them), and we suppose the edge costs to be partially ordered. C-semirings can represent multi-criteria MST problems, which are NP-hard to solve. Finally, we test one of the new algorithms to prove its applicability in practice, and we compare it with related work.

中文翻译：

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Kruskal带有嵌入式C指示器，以部分订购的成本解决MST问题

我们定义了两种基于代数的算法，用于求解边缘部分排序的最小生成树问题。我们建议的参数结构是c表示，可以同时表示不同的成本指标。我们将C-半音嵌入到Kruskal和反向删除Kruskal算法中（因此将它们概括化），并且我们假设边缘成本需要部分排序。C-semirings可以代表多标准MST问题，这是NP难以解决的。最后，我们测试一种新算法以证明其在实践中的适用性，并将其与相关工作进行比较。