title: Graphs and matroids weighted in a bounded incline algebra.
abstract: 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.
authors.affiliation: School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang 050031, China.
authors.forename: Ling-Xia
authors.initials: LX
authors.lastname: Lu
authors.affiliation: School of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China.
authors.forename: Bei
authors.initials: B
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D055641:Mathematical Concepts; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted