论文信息 - Maximal Empty Cuboids Among Points and Blocks

Maximal Empty Cuboids Among Points and Blocks

Abstract Given a three-dimensional box containing n points, we consider the problem of identifying all Maximal Empty Isothetic Cuboids (MEC) , i.e., all 3D empty parallelepiped bounded by six isothetic rectangular faces. It is shown that the total number of MECs is bounded by O ( n 3 ) in the worst case. An output-sensitive algorithm, based on plane-sweep paradigm, is proposed for generating all the MECs present on the floor. The algorithm runs in O ( C + n 2 log n ) time in the worst case, and requires O ( n ) space, where C is the number of MECs present inside the box.

Subhas C. Nandy | Bhargab B. Bhattacharya

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