A Multihomed customer will receive probably the whole BGP table from both service providers. He will then filter out routes inbound from the service provider. This kind of construct is flexible and scalable in the sense of less administrative burden.
The routers from the provider side have to send the complete BGP table, which must be then received and processed by the customer router, which then filters about 90% of the routes probably with a filter list. There is a lot of waste of resources which could be utilized elsewhere.
If the customer router could dynamically request a subset of routes from the provider will be the optimum solution to this problem. This situation could be solved with outbound route filtering (RFC 5291). The idea is to send the prefix list which the customer uses to filter towards the provider. Then the provider will filter the routes outbound.
Router R2 receives 4 networks via BGP 1.1.0/24, 1.1.1/24, 1.1.2/24 and 1.1.3/24. It then filters the networks 1.1.2/24 and 1.1.3/24 networks inbound with a prefx-list. The debug ip bgp updates in displays the effect.