1. Single source shortest paths in a simple polygon Guibas, Hershberger, Leven, Sharir, Tarjan (1987)

2. s

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13. s Single source shortest path tree in a simple polygon

14. s Assume a triangulation is given

15. s Traverse the dual tree

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20. There is a funnel associated with each leaf cusp

21. You split the funnel when processing the leaf

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31. Summary Scan the dual tree from the triangle that contains s Maintain a funnel at each leaf

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34. Summary (cont) Represent each funnel as a finger search tree

35. You split the funnel in time logarithmic in the size of the smaller piece. Then you insert an item to each piece

36. Summary (cont) The rest is analogous to the analysis of the jordan sorting algorithm