Most packing problems are NP-hard, and thus are typically attacked by approximation algorithms and fixed-parameter tractability, the two most recognized algorithmic paradigms for dealing with NP-hardness in theoretical computer science. This talk surveys recent developments on these two perspectives for packing problems. More concretely, I will talk about the following flavours of packing:
- (packing in geometry): how to pack polygons on the plane.
- (packing numbers): how to pack items into a knapsack to maximize the value.
- (packing in vector addition systems): how to reach your destination without running out of gas and money.