1. A method, comprising: storing, at a router, at least one neighbor table that indexes each of one or more Border Gateway Protocol (BGP) neighbors of the router by a respective virtual routing and forwarding instance identifier (VRF ID) that indicates a virtual routing and forwarding (VRF) instance associated with the BGP neighbor, each BGP neighbor being a network device with which the router establishes a BGP session; initiating a BGP update generation for a BGP table having one or more BGP network entries to be advertised, each entry having an associated VRF ID that indicates to which VRF instance the BGP entry is to be advertised; in response to initiating the BGP update generation, performing a single lookup operation into the neighbor table for each BGP entry based on the associated VRF ID of each BGP entry, to determine a corresponding VRF update group of indexed BGP neighbors to which each BGP entry is to be advertised; and generating a shared BGP update for each VRF update group for the initiated BGP update generation.