What structure does each link-state router build to describe routing costs to reach its destination networks?

Each link-state router builds a link-state database to describe the routing topology of the network, which includes detailed information about all the links to other routers and their states. This database enables the router to map the entire network topology it is aware of. From this link-state database, the router can then compute the shortest path first (SPF) tree using algorithms like Dijkstra's algorithm.

The shortest path first tree provides the routing paths based on the costs associated with reaching each destination network. Each router in the network independently generates its own SPF tree based on the shared link-state database, allowing it to determine the most efficient route to each destination.

In contrast, a routing table is used to store the best-known paths to various networks based on data that the router has gathered, but it is not the structure that is initially built from the link-state information. Similarly, a distance vector table is not applicable here as it pertains to distance vector protocols, which work differently than link-state protocols by sharing routing updates with neighbors rather than constructing a complete topology. The link-state database serves as the foundational dataset from which the SPF tree is created.