  A novel combination of established data analysis techniques for
reconstructing all charged-particle tracks in high energy collisions is
proposed. It uses all information available in a collision event while keeping
competing choices open as long as possible. Suitable track candidates are
selected by transforming measured hits to a binned, three- or four-dimensional,
track parameter space. It is accomplished by the use of templates taking
advantage of the translational and rotational symmetries of the detectors.
Track candidates and their corresponding hits, the nodes, form a usually highly
connected network, a bipartite graph, where we allow for multiple hit to track
assignments, edges. The graph is cut into very many minigraphs by removing a
few of its vulnerable components, edged and nodes. Finally the hits are
distributed among the track candidates by exploring a deterministic decision
tree. A depth-limited search is performed maximising the number of hits on
tracks, and minimising the sum of track-fit $\chi^2$. Simplified models of LHC
silicon trackers, as well as the relevant physics processes, are employed to
study the performance (efficiency, purity, timing) of the proposed method in
the case of single or many simultaneous proton-proton collisions (high pileup),
and for single heavy-ion collisions at the highest available energies.
