Routing:
Routing is the process of determining the path that data packets should take from the source to the destination in a computer network. It involves making decisions about the optimal routes based on various metrics and network conditions. Routing is a critical aspect of network communication as it ensures efficient and reliable data transfer.
Desirable Characteristics of Routing Algorithms:

Correctness: The routing algorithm should correctly determine the paths to destinations, ensuring that data reaches the intended recipients.

Simplicity: Routing algorithms should be simple to understand, implement, and maintain to facilitate efficient network management.

Robustness: The algorithm should be robust enough to handle changes in network topology, link failures, or other dynamic conditions.

Scalability: Routing algorithms should scale effectively with the size of the network, supporting a growing number of nodes and links.

Optimality: The algorithm should strive to find optimal paths based on predefined metrics, such as minimizing hop count, latency, or maximizing available bandwidth.

Adaptability: The routing algorithm should adapt to changes in the network, adjusting routes dynamically in response to varying conditions.
Distance Vector Routing:
Distance Vector Routing is a type of routing algorithm where each node maintains a table (vector) that contains the distance (cost) to every other node in the network. The distance vector is periodically exchanged with neighboring nodes. A common distance vector algorithm is the BellmanFord algorithm.
Example:
Consider a small network with four nodes (A, B, C, D) and the following initial distance vector table for node A:
Destination 
Cost (A to Destination) 
A 
0 
B 
1 
C 
3 
D 
∞ 

In this table, the cost from A to A is 0, and the cost to B, C, and D is initially set to 1, 3, and infinity (∞), respectively.

Node A periodically shares its distance vector with its neighbors (B, C, D).

Upon receiving the distance vectors from its neighbors, A updates its own distance vector based on the received information and the known costs.

This process repeats iteratively until convergence, with nodes updating their distance vectors and exchanging information until a consistent and stable routing table is achieved.

The algorithm aims to minimize the cost to reach each destination and converge to a state where no further updates are needed.