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Vector network analysis
GRASS provides support for vector network analysis. The following algorithms are implemented:

    * Vector maintenance: v.net
    * Shortest path: d.path and v.net.path
    * Traveling salesman (round trip): v.net.salesman
    * Allocation of sources (create subnetworks, e.g. police station zones): v.net.alloc
    * Minimum Steiner trees (star-like connections, e.g. broadband cable connections): v.net.steiner
    * Iso-distances (from centers): v.net.iso

Vector directions are defined by the digitizing direction (a-->--b). Both directions are supported, network modules provide parameters to assign attribute columns to the forward and backward direction.

Vector networks: Linear reference system (LRS)
LRS uses linear features and distance measured along those features to positionate objects. There are the commands v.lrs.create to create a linear reference system, v.lrs.label to create stationing on the LRS, v.lrs.segment to create points/segments on LRS, and v.lrs.where to find line id and real km+offset for given points in vector map using linear reference system.

The LRS tutorial explains further details.