Abstract
To judge the loop-nonnegativity of a matrix over an idempotent semiring and compute the plus-closure of when it is loop-nonnegative, a Plus_Closure_of_Matrix algorithm of complexity is constructed and proved. As a generalization of Floyd algorithm, Warshall algorithm as well as Gauβ-Jordan Elimination algorithm on idempotent semirings, this algorithm can also be used to solve some Algebraic Path Problems, Shortest Path Problems and the transitive closures of matrices over idempotent semirings even if the idempotent semirings have no completeness and closeness.
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