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#ALGORITHMS!

Join the chat at https://gitter.im/hallfox/AlgoProject

#Usage The program can be setup by typing make and then running the astar program in the bin directory. New graphs can be generated by typing make graphs. If you just want to build the graph generator program, type make tests.

Credit for the graph generation program goes to Seth Pettie pettie@mpi-sb.mpg.de and Vijava Ramachandran vlr@cs.utexas.edu. More details can be found in gen/README.txt. Found on http://www.dis.uniroma1.it/challenge9/download.shtml#benchmark.

Ideas:

  • Finding communities in a graph
  • A* search algorithm and comparison to Dijkstra

#Proposal

We will implement and evaluate the A* shortest paths algorithm. This algorithm finds the shortest path between any two nodes in a graph and can operate faster than Dijkstra's algorithm. This is because A* is built on top of Dijkstra's algorithm with added heuristics.

Because of this we will implement the following:

  • Adjacency List Graph (Sparse) (Taylor Foxhall)
  • Adjacency Matrix Graph (Dense) (Armond St. Juste)
  • Dikjstra's Algorithm for shortest paths (Alexander Strong)
  • A* Heuristic function and A* search (all)

We will evaluate A* and how it compares with Dijkstra by measuring the run time to find the shortest path. The parameters we will test with include:

  • Dense adj matrix graph
  • Sparse adj matrix graph
  • Dense adj list graph
  • Sparse adj list graph
  • Mixed adj matrix graph
  • Mixed adj list graph

Additionally as we learn more about the structure of A* we will look for certain optimizations to A* and test to see how the above parameters affect the runtime.

#Test Case Format

Test cases will begin with an integer N, the number of vertices on the first line. The following lines will contain a value V, which will be the value of a vertex followed by E the vertex connected to it, then a weight W. The file is terminated by a -1.

#Test Cases

  • grid graph
    • 200, 1000, 5000 nodes (maybe more depending on results)
  • toroid graph (2D, 3D)
  • general geometric-oriented graphs
  • sparse
  • dense
  • adjacency lists
  • adjacency matrix

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