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According to my knowledge, Mater-Slave election is needed to decide who will to start communication between two routers. In broadcast domains all the DR other routers communicate with DR. Is there a need for M/S election here?

Please clarify.

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The election is part of the process for database exchange. Since every router in the broadcast domain creates a full adjacency with the DR and BDR, they determine a master/slave state with the DR/BDR.

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...In broadcast domains all the DR other routers communicate with DR. Is there a need for M/S election here?

Yes, a M/S election is needed. Since the router does not know how many neighbors are on the attached circuit it has to send LSA updates via multicast. On point-to-point Interfaces a unicast adress is used. This is one example why a M/S election is needed on broadcast and NBMA interfaces.

For this particular example I suggest reading the OSPF Version 2 flooding procedure in RFC 2328

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