5.04-1. Bellman Ford Algorithm (1, part 1). Consider the scenario shown below, where at t=1, node e receives distance vectors from neighboring nodes d, b, h and f. The (old) distance vector at e (the node at the center of the network) is also shown, before receiving the new distance vector from its neighbors. Indicate which of the components of new distance vector at e below have a value of 1 after e has received the distance vectors from its neighbors and updated its own distance vector. ## Distance Vector Routing Example at Time t=1### Scenario:At time \( t=1 \), node \( e \) receives distance vectors (DVs) from nodes \( b, d, f, \) and \( h \).### Objective:Determine the new distance vector (DV) computed at node \( e \) at \( t=1 \).### Node Connections and Costs:- **Node Connections:** - \( a \) is connected to \( b \) (cost 8). - \( b \) is connected to \( c \) (cost 1). - \( b \) is connected to \( e \) (cost 1). - \( d \) is connected to \( e \) (cost 1). - \( d \) is connected to \( f \) (cost 1). - \( f \) is connected to \( e \) (cost 1). - \( g \) is connected to \( h \) (cost 1). - \( h \) is connected to \( i \) (cost 1).### Received Distance Vectors:- **From Node \( b \):** - \( D_b(a) = 8 \) - \( D_b(c) = 1 \) - \( D_b(d) = \infty \) - \( D_b(e) = 0 \) - \( D_b(f) = \infty \) - \( D_b(g) = \infty \) - \( D_b(h) = \infty \) - \( D_b(i) = \infty \)- **From Node \( d \):** - \( D_d(a) = 1 \) - \( D_d(b) = \infty \) - \( D_d(c) = \infty \) - \( D_d(e) = 1 \) - \( D_d(f) = 1 \) - \( D_d(g) = \infty \) - \( D_d(h) = 1 \) - \( D_d(i) = \infty \)- **From Node \( f \):** - \( D_f(a) = \infty \) - \( D_f(b) = \infty \) - \( D_f(c) = \

The Bellman-Ford algorithm is a fundamental algorithm in graph theory and network analysis. Named after mathematicians Richard Bellman and Lester Ford, the algorithm is designed to find the shortest paths from a source node to all other nodes in a weighted graph, even when the graph contains edges with negative weights.Here's an introduction to the Bellman-Ford algorithm:Objective:The primary goal of the Bellman-Ford algorithm is to determine the shortest paths and their corresponding distances from a single source node to all other nodes in a graph.Algorithm Steps:1. Initialization: Set the distance from the source node to itself as 0 and all other distances to infinity.2. Iterative Relaxation: Iterate through all edges in the graph and update the distances if a shorter path is found.3. Repeat: Repeat the iterative relaxation step until no further updates can be made. In the worst case, this requires iterations, where is the number of vertices in the graph. Let's break down the explanation of the Bellman-Ford algorithm application in the context you provided:1. Given Information: - The scenario involves a network where each node maintains a distance vector, which is essentially a list of distances from that node to every other node in the network. - At time , node 'e' receives new distance vectors from its neighboring nodes 'd', 'b', 'h', and 'f'. - The initial (old) distance vector at node 'e' before receiving the updates is provided.2. Old Distance Vector at Node 'e': - The old distance vector at node 'e' at time is initially set to . This vector represents the distances from 'e' to all other nodes, with '0' at the positions corresponding to 'g' and 'i'.3. Distances Received at : - Node 'e' receives distance values from its neighbors, including 'd' and 'h'. However, specific values are not provided in your question. These received distances are then used to update the distance vector at 'e'.4. Distances from Neighbors (Partial Update): - The distances from neighbors 'b', 'd', 'f', and 'h' are used to update the distance vector at 'e'. - For example, is not updated, remains '0', , is updated with the distance received from 'd', is updated with the distance received from 'f', remains '0', is not updated, and remains '0'.5. Answering Questions: - Specific values for , , , and are not provided, so they remain unknown. - Some specific values, like and , are given as '0' and respectively.6. New Distance Vector at Node 'e' at : - The final updated distance vector at 'e' is provided as . - This represents the distances from 'e' to all other nodes after processing the received information.In summary, the Bellman-Ford algorithm is employed to iteratively update distance vectors at each node in the network based on information received from neighbors, ensuring that each node converges to the correct shortest paths and distances from the source node ('e' in this case) to all other nodes.is updated to 0 as it is received from a. remains 0. remains ∞ as it is not received from any neighbor. remains ∞ as it is not received from d at t=1. is updated to 1 as it is received from f. remains 0. remains ∞ as it is not received from any neighbor. remains 0.This represents the new distance vector at node 'e' after it receives and processes the distance vectors from its neighbors at time t=1.

Engineering

Data Structures and Algorithms

5.04-1. Bellman Ford Algorithm (1, part 1). Consider the scenario shown below, where at t=1, node e receives distance vectors from neighboring nodes d, b, h and f. The (old) distance vector at e (the node at the center of the network) is also shown, before receiving the new distance vector from its neighbors. Indicate which of the components of new distance vector at e below have a value of 1 after e has received the distance vectors from its neighbors and updated its own distance vector.

5.04-1. Bellman Ford Algorithm (1, part 1). Consider the scenario shown below, where at t=1, node e receives distance vectors from neighboring nodes d, b, h and f. The (old) distance vector at e (the node at the center of the network) is also shown, before receiving the new distance vector from its neighbors. Indicate which of the components of new distance vector at e below have a value of 1 after e has received the distance vectors from its neighbors and updated its own distance vector.