Single source shortest paths in a simple polygon

Guibas, Hershberger, Leven, Sharir, Tarjan (1987)

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Single source shortest path tree in a simple polygon

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Assume a triangulation is given

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Traverse the dual tree

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There is a funnel associated with each leaf

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You split the funnel when processing the leaf

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Summary

• Scan the dual tree from the triangle that contains s

• Maintain a funnel at each leaf

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Summary (cont)

• Represent each funnel as a finger search tree

You split the funnel in time logarithmic in the size of the smaller piece.

Then you insert an item to each piece

Summary (cont)

• The rest is analogous to the analysis of the jordan sorting algorithm