Minimum Membership Covering and Hitting

Set Cover is a well-studied problem with application in many fields. A well-known variant of this the Minimum Membership problem: Given set points and objects, objective to cover all while minimizing maximum number objects that contain any one point. dual Hitting stab an object contains. We study both these variants geometric setting various types plane, including axis-parallel line segments, strips, rectangles are anchored on horizontal from side, stabbed by line, two lines (i.e., each rectangle shares its top or bottom edge (or both) input lines). For problems we either prove NP-hardness give polynomial-time algorithm. In particular, show it NP-complete decide whether there exists solution depth exactly 1 for problem. addition, generalized version