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2 - marks * conditions involved in floyd's algorithm * residual network in flow of network * characterisitics of transportation network

Question

2 - marks

  • conditions involved in floyd's algorithm
  • residual network in flow of network
  • characterisitics of transportation network
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Solution

  1. Conditions involved in Floyd's Algorithm:

    • Floyd's algorithm is used for finding the shortest paths between all pairs of vertices in a weighted graph with positive or negative edge weights.
    • The graph must be directed and connected.
    • The algorithm works by repeatedly improving an estimate on the shortest path between two vertices, until ultimately obtaining the shortest path.
    • It uses a matrix to store the shortest distances between every pair of vertices.
  2. Residual Network in Flow of Network:

    • A residual network is derived from a given flow network and a flow.
    • It consists of edges with capacities equal to the remaining capacity (original capacity - flow) of the corresponding edges in the flow network.
    • The residual network can have an edge not in the original graph, if there is a positive flow on the edge in the original graph.
    • It is used in algorithms like Ford-Fulkerson to find the maximum flow in a network.
  3. Characteristics of Transportation Network:

    • A transportation network is a network where nodes represent locations and edges represent routes between locations.
    • Each edge has a weight, which could represent distance, cost, time, or any other relevant factor.
    • The network is typically directed, meaning that travel from location A to location B does not necessarily imply that travel from B to A is possible.
    • The goal in a transportation network is often to find the shortest or least expensive route from one location to another.

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