Single source shortest paths in a simple polygon

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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
cusp
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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

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You split the funnel in time logarithmic in the
size of the smaller piece. Then you insert an
item to each piece
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Summary (cont)

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

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