• To reduce the complexity of finding a collsion-free path by reducing the free space.
• Creation of a subvisibility graph from the visibility graph.
• Use the smaller subvisibility graph to determine the shortest collision-free path.
• Use of the smaller graph reduces the complexity of computing the visibility graph for a greater amount of free space, consequently having to compute visibility edges for obstacles that are not in the direct path between the robot and target.

Algorithm
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Please enable Java for an interactive construction (with Cinderella). Begin by defining a straight line from start vertex 'S' to terminal vertex 'T'.

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Please enable Java for an interactive construction (with Cinderella). Position obstacle1, O₁, where it belongs and if O₁ overlaps segment ST, then delete segment ST and create segments S_iO_i and T_iO_i where i is a vertex in O₁, for all i if visible to S or T.

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Please enable Java for an interactive construction (with Cinderella). Continue for all O_i in a list of obstacles performing visibility graph algorithm only when each additional O_i overlaps an existing segment.
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Please enable Java for an interactive construction (with Cinderella). The end result will be a subvisibility graph which will work on only the obstacles that are in the direct path of segment ST, thereby reducing the overall complexity of the free space to a "sub" smaller free space.

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