| Summary: | In max-plus algebra, some algorithms for determining the eigenvector of irreducible matrices are the power algorithm and the Kleene star algorithm. In this research, a modified Kleene star algorithm will be discussed to compensate for the disadvantages of the Kleene star algorithm. The Kleene star algorithm’s time complexity is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mrow><mo>(</mo><mrow><mi>n</mi><mrow><mo>(</mo><mrow><mi>n</mi><mo>!</mo></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and the new Kleene star algorithm’s time complexity is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mrow><mo>(</mo><mrow><msup><mi>n</mi><mn>4</mn></msup></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, while the power algorithm’s time complexity cannot be calculated. This research also applies max-plus algebra in a railroad network scheduling problem, constructing a graphical user interface to perform schedule calculations quickly and easily.
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