Minimum cell connection and separation in line segment arrangements

We study the complexity of the following cell connection and separation problems in segment arrangements. Given a set of straight-line segments in the plane and two points a and b: (i) compute the minimum number of segments one needs to remove so that there is a path connecting a to b that does not intersect any of the remaining segments; (ii) compute the minimum number of segments one needs to remove so that the arrangement induced by the remaining segments has a single cell; (iii) compute the minimum number of segments one needs to retain so that any path connecting a to b intersects some of the retained segments. We show that problems (i) and (ii) are NP-hard, while problem (iii) is polynomialtime solvable. We also discuss special polynomial-time and xed-parameter tractable cases.

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