We illustrate usage of the chain level Floer theory, which is the Floer theoretic version of classical mini-max theory for indefinite functionals, in the study of length minimizing property of geodesics on the Hamiltonian diffeomorphism group. As an example, we prove that any quasi-autonomous Hamiltonian path is length minimizing in its homotopy class with fixed ends, as long as it does not allow any periodic orbits of period less than one. This generalizes the results on the autonomous case by Hofer (C n ) and by McDuffSlimowitz (in general). If time permits, we will also explain how to use this chain level Floer theory to construct a new invariant norm of Viterbo’s type on the Hamiltonian diffeomorphism group of arbitrary closed symplectic manifolds