COS 226 Programming Assignment 9 - Checklist

Checklist 9: Shortest paths.

The following is a checklist which provides a summary of the assignment. This is meant only as a supplement; please read the original assignment description.

  • Frequently Asked Questions
  • Help with Java
  • Overview
  • Requirements
    •

    Frequently Asked Questions:
    (This is the only part of this checklist which will change during the week.)

    [April 29] For a full range of methods dealing with random number generation, you may want to use the class java.util.Random which has documentation at http://java.sun.com/docs/books/jls/html/javautil.doc9.html#7616

    [April 28] It has been settled: the two-way search as described in the assignment does not necessarily return the true shortest path. There is an easy way to fix the algorithm, however it is too close to the deadline for us to change the assignment requirements. Instead, we will offer one extra credit point for implementing the correct algorithm. As always, if you do the extra credit, please mention this in your readme file.

    [April 27] What do we mean by "number of nodes examined"? It is not very clear cut. Let's suggest the following standard: Report the number of nodes which have been added to the tree(s). (if you have already written your code to count some other meaningful interpretation, go right ahead. Just put a big note in the readme to explain what it is that you are reporting.)

    [April 27] If you want a much more interesting set of test graphs for the various heuristics in this assignment, try using this modified Graph constructor based on the new class Fence.java.

    [April 27] If you want to get rid of the "deprecated" warnings during compilation, replace all occurrences of getClipRect with GetClipBounds in the files Graph.java and demo.java. (webster defined "deprecate" as "belittle" or "disparage", and we won't stand to be disparaged)

    [April 27] A hint on Step 3: for the preprocessing step, you should be thinking about a new graph with M^2 nodes.

    [April 25, corrected April 27] For those students using Program 9.12 of the text, please note that there was a bug in the early printings which has only been fixed in the fourth printing. The last line of the exch routine should read
    t=pq[qp[i]];pq[qp[i]]=pq[qp[j]]; pq[qp[j]]=t;

    Help with Java: There are many possible sources for those needing help learning Java. We can recommend a few,
  • The COS126 Lecture notes on Java (part 1,part 2)
  • A Java Tutorial (from www.javasoft.com or java.sun.com)
    • Overview: This week, the assignment has asked you to solve the shortest path problem in one of three ways (each way requires additional programming, but should result in a better algorithm) You should only turn in one program.

    Here we give an overview of the three steps. (specific requirements of your submissions will be in the following section)

  • Step 1: (you will receive up to 6 points if this step is the only one you complete)
    Compute the shortest path between two points of a graph by using the priority-first search method. The priority of a fringe node should equal the shortest observed path from the source to that node. (see lecture notes for details).

  • Step 2: (you will receive up to 8 points if you completely only the first two steps)
    This step actually consists of two improvements. The first one is essentially a "one-liner" but will already make great improvement in your search. Use the priority-first search, but change the definition of the priority for a fringe node to equal the sum of the shortest observed path in the graph from the source to that node together with the "as-the-crow-flies" distance from the fringe node to the goal. (For those interested in a proof of why this method will still find the correct shortest path, come talk to us)

    After making that change, the other improvement is the following. Do the modified search from both the source and the destination at the same time (i.e. alternate taking turns expanding). As soon as there is any node which has been visited by both searches, stop and return the shortest path which combines the paths from the source to this point and from the point to the destination. (Again...does this work? We certainly hope so!)

  • Step 3: (You will receive up to 10 points if you complete all three steps)
    In the previous step we used the "as-the-crow-flies" distance as a rough estimate of how far a fringe node is from the goal when walking along the graph. In this step we will spend a bit of preprocessing time in order to get a more accurate estimate to use.

    Consider dividing the space into an M-by-M grid. Temporarily, assume that all nodes in the same grid cell are at distance zero from each other, but that to walk between grid cells, you must walk along one of the original graph edges between a node in one cell and a node in the other. For any two cells, compute the distance of the shortest path which connects a node of one cell to a node of the other. (Truly, you only need to compute this for pairs of cells where one of the cells contains either the source node or the destination node). Once you have pre-computed these new estimates between cells, modify the method from Step 2 to replace the "as-the-crow-flies" estimate with this new estimate of the distance between the cell containing the fringe node and the cell containing the goal. (Obviously your choice of the value of M will have to balance the preprocessing time with the improvement during the search)

    • Requirements: No matter which method you turn in, the following is required of your program:
  • After creating the graph, either allow the user to specify the source node and the destination node, or else pick both of these nodes at random.
  • Your algorithm should NOT search the entire graph, rather it should stop as soon as the shortest path between the two nodes has been found.
  • Graphically, you are required to at least do the following:
  • draw the entire original graph.
  • highlight, using some other color, all edges/nodes which your search considered.
  • highlight, using yet another color, the eventual shortest path which was found.
  • leave the final picture on the screen for at least 5 seconds (before quitting or restarting).
    • (obviously, there is a good deal of freedom in how you choose to animate your method).
  • Textually, you must output at least the following:
  • The number of nodes which the search examined.
  • readme Analyze the performance of your method for graphs of V nodes for various values of V, and formulate a hypothesis about the number of nodes that your method examines to find the shortest path between two random nodes, on the average, as a function of V.

    If you implement several of the methods along the way, please also give a brief discussion of the number of nodes examined by the earlier methods (to see if all of the additional work paid off).

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    Last modified: April 29, 1999