PDF constraints and $\alpha_{S}$ from CMS

The measurement of the strong coupling constant based on four different observables is presented. The four observables are the inclusive jet spectrum, the 3-jet production cross section, the ratio of the inclusive 3-jet cross section to the inclusive 2-jet cross section, and the top quark pair production cross section in the dilepton channel. The data samples used for these measurements were collected at a proton-proton centre-of-mass energy of 7 TeV with the CMS detector at the LHC. The extracted values of the strong coupling constant are in good agreement with the world average value and the running of the strong coupling is confirmed for the first time at the TeV region. Additionally, results on constraining the gluon and the valence-quark PDFs using the inclusive jet spectrum and the muon charge asymmetry in the inclusive W production are also presented.