Comment by cbhl

It's pretty easy to imagine a counter-example that would have you traverse the length of the map, when the best route would be to detour on an existing traversal. Consider:

    1...2...3...4...5
    7...............6
    8.......9........
    13..12.....11..10

versus

    1...2...3...4...5
    13..............6
    12......9........
    11..10......8...7