I wonder if we can solve the shortest-path with a space filling curve or is there a better solution? How good would be the approximation compared to an exact solver? The graph doesn't need to satisfy the triangle inequality.
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Do you have some constraints/goals that make A* or Dijkstra's algorithm not applicable? – Kornel Jun 14 '13 at 10:26
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A* with good heuristic function is generally the best solution (in terms of speed and finding shortest path).
I'm not sure what do you want to achieve with space-filling curve. I suppose it could give you interesting path in areas where costs are equal.
Kornel
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Note that the heuristic must be an admissible heuristic in order to get the actual shortest-path. This is not always easy to do. – Maxime Chéramy Jun 14 '13 at 10:26