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The $K_\perp~$ algorithm The $K_\perp~$algorithm can function in several distinct ways depending on the nature of the colliding beams and the physics to be studied. We deal first with hadron-hadron and lepton-hadron collisions. There are two modes of operation, the `inclusive' and `exclusive' modes. The difference between the two cases, described in sections 2.1 and 2.2, is in the definition of the hard final state jets, and the separation of these jets from the beam remnants. For the analysis of ${e^+ e^-}~$data, in contrast, there is of course no concept of beam remnants. The algorithm proceeds in a very similar way to that employed in a jet substructure analysis. We deal with these two cases together in section 2.3.