# Aggregation Algebras

 Title: Aggregation Algebras Author: Walter Guttmann Submission date: 2018-09-15 Abstract: We develop algebras for aggregation and minimisation for weight matrices and for edge weights in graphs. We verify the correctness of Prim's and Kruskal's minimum spanning tree algorithms based on these algebras. We also show numerous instances of these algebras based on linearly ordered commutative semigroups. BibTeX: @article{Aggregation_Algebras-AFP, author = {Walter Guttmann}, title = {Aggregation Algebras}, journal = {Archive of Formal Proofs}, month = sep, year = 2018, note = {\url{https://isa-afp.org/entries/Aggregation_Algebras.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Stone_Kleene_Relation_Algebras Used by: Relational_Minimum_Spanning_Trees Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.