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On Computing Connected Components of Line Segments
April 1995 (vol. 44 no. 4)
pp. 597-601

Abstract—It is shown that given a set of n line segments, their connected components can be computed in time O(n4/3log3n). A bound of o(n4/3) for this problem would imply a similar bound for detecting, for a given set of n points and n lines, whether some point lies on some of the lines. This problem, known as Hopcroft’s problem, is believed to have a lower bound of Ω(n4/3). For the special case when for each segment both endpoints fall inside the same face of the arrangement induced by the set of segments, we give an algorithm that runs in O(nlog 3n) time.

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Index Terms:
Connected components, line segments, nets, Hopcroft’s problem.
Ramakrishna Thurimella, Mario Alberto Lopez, "On Computing Connected Components of Line Segments," IEEE Transactions on Computers, vol. 44, no. 4, pp. 597-601, April 1995, doi:10.1109/12.376174
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