Why are the routes with smaller costs passing through the backbone area not preferred

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OSPF defined by RFC 2328 must be backward compatible with RFC 1583. As specified in RFC 2328, if "RFC1583 Compatibility" is disabled, when routes can be learnt through common areas and the backbone area, the routes learnt through common areas are preferred regardless of their costs. This is to reduce the burden on the backbone area.

Other related questions:
Why OSPF on an S series switch does not preferentially select a route with a small cost value and through the backbone area
OSPF defined by RFC 2328 must be compatible with RFC 1583. As defined in RFC 2328, if "RFC1583 Compatibility" is disabled, the routes learned through common areas are preferred regardless of their costs when routes can be learned through common areas and the backbone area. This helps reduce the burden of the backbone area.

Do problems occur in route calculation when the backbone area is discontinuous
If the backbone area is discontinuous, the networks in some areas may be unreachable and routing loops may occur in inter-area routes and external routes.

How do I view the OSPF cost and Preference on the AR router
The display ospf lsdb command displays OSPF LSDB information. The display ospf brief command displays brieft OSPF information.

Can an S series switch correctly calculate routes when OSPF backbone areas are not continuous
For S series switches supporting OSPF, if OSPF backbone areas are not continuous, some areas may be unreachable and loops may occur on inter-area and external routes.

Why the ASBR does not generate equal-cost route
Two areas are configured on two devices separately, for example: SwitchA: area 0: 10.5.5.5 area 1: 10.4.4.4 SwitchB: area 0: 10.5.5.6 area 1: 10.4.4.6 Adjacencies are formed on the devices separately. Thus, the next-hop of a route that SwitchB learns from SwitchA should be 10.5.5.5 or 10.4.4.4. However, the route on SwitchB goes through only 10.4.4.4 in area 1 as the gateway and no load sharing can be performed. This is because when multiple equal-cost routes exist, an ASBR selects the route with the greatest area ID.

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