Hello ima,
A very good question!
The LSA1 represents a particular router and its links to other network infrastructure objects it can directly talk to (i.e. is directly connected to). The LSA1 therefore does represent a topological relation of a router to another router or to another network. Each object that a particular router is connected to should be indicated in that router's LSA1.
However, this has a certain disadvantage. Imagine you have an Ethernet switch with 10 routers connected to it. Each router can hear the other 9 routers and can talk to them directly. With the LSA1 as described earlier, each router would have to indicate, among other things, 9 links to other routers on this common segment. Each of the LSA1 of these 10 routers would need to contain, apart from other links, also 9 references to other router's LSA1 on the common segment. In the topological database, only describing the common network between these routers would result in recording 10*9 = 90 links (or edges, as we sometimes call them). With N routers on the same segment, this approach would lead to N*(N-1) links, a quadratic memory footprint. This is, by the way, the exact idea behind the point-to-multipoint OSPF network type.
So the authors of OSPF chose a different approach. Instead of each router on a common segment declaring links to each remaining router, the common network itself is represented as a separate standalone object in the link-state database. Each router would need to indicate only one link to the network, irrespective of the total number of the routers in that network. The network object would then indicate a link to each router connected to the same network. This is exactly the idea of LSA2 - it represents the common multiaccess network and attached routers. This way, each router has only one link regarding this segment in its LSA1, and the LSA2 has N links towards each member router of the network. The memory footprint has now been reduced from O(N^2) to O(N), an order of magnitude lower. At the cost of having an extra object in the link-state database, the number of links has significantly decreased. With a network of 10 routers, this would mean 10 (in LSA1) + 10 (in LSA2) = 20 links in total describing the common segment. Compare that to 90 links from the previous approach.
The task of creating the LSA2 into the link-state database is given to the Designated Router, and in fact, this is its main purpose. The synchronization responsibility is just an add-on, but the task of advertising an LSA2 for a multiaccess network is crucial.
So the LSA2 exists to decrease the number of links necessary to describe a multiaccess segment in the link-state database. While using only LSA1 would be possible, the memory footprint of the link-state database would grow quadratically and so would the time necessary to run the SPF over such database. With the LSA2 representing a particular multiaccess segment, the memory footprint grows linearly with the number of routers on the segment, a significant saving especially with networks with larger counts of routers on common segments.
Please feel welcome to ask further!
Best regards,
Peter
