Assuming dark matter particles can be pair-produced at the LHC from cascade decays of heavy particles, we investigate strategies to identify the event topologies based on the kinematic information of final state visible particles. This should be the first step towards measuring the masses and spins of the new particles in the decay chains including the dark matter particle. As a concrete example, we study in detail the final states with 4 jets plus missing energy. This is a particularly challenging scenario because of large experimental smearing effects and no fundamental distinction among the 4 jets. Based on the fact that the invariant mass of particles on the same decay chain has an end point in its distribution, we define several functions which can distinguish different topologies depending on whether they exhibit the end-point structure. We show that all possible topologies (e.g., two jets on each decay chain or three jets on one chain and the other jet on the other chain, and so on) in principle can be identified from the distributions of these functions of the visible particle momenta. We also consider cases with one jet from the initial state radiation as well as off-shell decays. Our studies show that the event topology may be identified with as few as several hundred signal events after basic cuts. The method can be readily generalized to other event topologies. In particular, event topologies including leptons will be easier because the end points are expected to be sharper and there are more distinct invariant mass distributions from different charges. Show Partial Abstract