1. Pathfinding Algorithms for Mutating Weight Graphs Haitao Mao Computer Systems Lab 2007-2008

2. The Pathfinding Problem Given a weighted graph, its weight mutation history, a start vertex, and a destination vertex, find the best vertex to move to next

3. Sample Input 5 7 0 4 5 (vertices, edges, start vertex, end vertex, history length)‏ 0 1 2 (first vertex, second vertex, edge weight)‏ 2.2 (history at a timestep for this edge)‏ 4 more history points Data for the other 6 edges of the graph

4. Preliminary Algorithm Heap Dijkstra Take the closest point to the start that has not been visited Update minimum weights to neighbors of that vertex Use a heap to decrease runtime Does not use history

5. History Class Takes in all the data for one edge and makes a hash table Uses a heuristic function to weight the timesteps based on distance of initial value of that timestep and current value Predicts future mutations

6. Algorithm For each timestep, for each vertex, use history class and randomized distance to determine best previous vertex – lots of complexities here Backtrack to find best vertex for first timestep Unsure of optimal heuristic function, but 1/(1+d^n) works pretty well for 3<n<4.

7. Next quarter Problem may need to be simplified to eliminiate some of the complexities in the algorithm – currently too many variables and complications to deal with. Comparison analysis of different algorithms Graph generator and massive testing