Design and Analysis of Algorithms

CSE 5311 Section 087/088/098 Fall 2002

Program 3

Due: November 26, 2002 (midnight)

For this assignment you will write a program that determines the shortest routes for messages between two nodes in a dynamic network of nodes and connections. Your program will also support pruning the network to a minimum spanning tree to help minimize connections. The specifics of the program follow. All code must be written by you individually and may not be copied in whole or in part from other sources.

  1. Your program will implement a graph data structure to represent the dynamic network, where vertices are nodes, and edges are connections between nodes. The data structure should support the addition and deletion of nodes and connections. Connections are bidirectional. Each connection (u,v) has a weight w(u,v) representing the delay in milliseconds of the connection. There is at most one connection between two nodes.

  2. Your program will implement an algorithm to compute the shortest path and distance between two nodes. Be sure to describe in the comment to this algorithm what technique you are using for the computation.

  3. Your program will implement an algorithm for finding the minimum spanning tree of the network, identifying connections to delete to result in a minimum spanning tree.

  4. The main part of your program will read in and process commands from a file whose name is given as a command-line argument. Each line of the input file contains one of the following commands. All command arguments are positive integers.

    CommandDescription
    add n Add node numbered n to network. Output whether node added or already existed in the network.
    delete n Delete node n from the network along with all its connections. Output whether node does not exist in network or the node and connections deleted.
    connect n1 n2 w Add a connection between nodes n1 and n2 with weight w. Output whether new connection added, weight changed, or already exists.
    disconnect n1 n2 Delete connection between nodes n1 and n2. Output whether connection deleted or does not exist in network.
    message n1 n2 Find the shortest route from node n1 to node n2. Output whether the route exists and, if so, the sequence of nodes and total delay of the route.
    print Print all the connections in the network in the form n1 --w-- n2, one per line, where n1 < n2. If a node has no connections, then output just the node n1. The output should be in increasing order by first node number, and then by second node number.
    prune Find and delete the connections necessary to yield a minimum spanning tree. If the network is not a connected graph, then just output "Network not connected." Otherwise, either output that it is already a minimum spanning tree or output the connections deleted.

  5. See pgm3.in and pgm3.out for sample input and output. Your output should follow the sample as closely as possible.

  6. After ensuring that your program compiles and runs correctly on the omega.uta.edu system, submit your source code to me (holder@cse.uta.edu) by the above deadline. Please only send one email message; use attachments if sending multiple files. In addition to correct functionality and satisfaction of the above constraints, your submission will be graded based on good programming style and documentation.