Graphs and Matroids Weighted in a Bounded Incline Algebra

الملخص EN

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem.

The solutions for LPP and related algorithms are given.

Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.