SPF is run against an OSPF area's link topology. How the resultant cost analysis is applied can vary based on the type of route. For instance, an E2 type external only has its injected cost, i.e. the SPF cost is ignored, but for an E1 type external, the SPF calculated cost to the ASBR is added to the injected cost.
SPF should be run only for the routes within that area. For routes belonging to other area, the nearest ABR is calculated acc to the SPF of the same area. Running SPF for the link state topology of the complete ospf domain will cause SPF to be re-calculated for any change in link status in any remote areas. This would defeat the purpose of having areas. The SPF calculation should therefore be only for the specific area. For inter-area routes only the nearest ABR should be calculated and the shortest path within that area will be calculated by routers in that area.
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