C-semiring Frameworks for Minimum Spanning Tree Problems

In this paper we define general algebraic frameworks for the Minimum Spanning Tree problem based on the structure of c-semirings. We propose general algorithms that can compute such trees by following different cost criteria, which must be all specific instantiation of c-semirings. Our algorithms are extensions of well-known procedures, as Prim or Kruskal, and show the expressivity of these algebraic structures. They can deal also with partially-ordered costs on the edges.

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