Graph Algorithms: Everything is in Order 

The talk begins with a survey of order-theoretic properties of graph classes that have consequences on computational problems in graphs, including some own old results from around 1990, and then it jumps to a more recent use (2020) of such properties for a motion planning problem called Patrolling. It continues with other path planning and layout planning problems that I dealt with in my work at the Fraunhofer-Chalmers Research Centre for Industrial Mathematics, and with thoughts about algorithm design "on paper" versus real-world use cases. The talk will focus on concepts, problems, and ideas, and will not go deeply into technical details of the considered algorithms.