Routers direct traffic between networks or subnetworks, for this they operate at Layer 3, the network layer, of the OSI Model. Routers don't track individual computers, but they contain a routing table and other information which allows them identify the best path to take and transporting a packet to get to its destination.
Distance Vector routing uses RIP (Routing Information Protocol) or RIP2 routing protocol. Both of these protocols use the hop count as their routing metric. RIP allows a maximum of 15 hops from source to a destination. This prevents routing loops. Distance vector routers exchange routing table information with other routers on a regular schedule.
Link State routing is an improvement over Distance Vector routing. Link State routing protocols such as OSPF (Open Shortest Path First) and IS-IS (Intermediate System to Intermediate System) use statistics like number of hops, distance, link speed, and traffic to calculate the cost of different routes through the Internet. They use Dijkstra's algorithm to determine the lowest cost route. Link State routers exchange routing table information only when their tables change.
Convergence is the state of when a group of routers have exchanged routing table information so that they all have the same topological information about the network. The goal of any routing protocol is to achieve convergence as quickly as possible and with the least amount of overhead.
Since Link State routing needs to exchange routing table information only when there is a change in the network, it requires less transmission overhead to achieve convergence. However it requires more processing and more powerful routers.
Hybrid routing has the advantages of both distance vector and link state protocols. It uses distance vector protocol to reduce the processing power requirement, but exchanges routing table information only when their tables change to reduce transmission overhead.
Today, many modern routing protocols that don't conform strictly to distance vector routing or link state routing are referred to as Hybrid Routing Protocols, but they actually use and exchange a variety of network statistics used to calculate the cost of different routes through the Internet.
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