Minimum d-convex partition of a multidimensional polyhedron with holes

Abstract

In a normed space Rn over the field of real numbers R, which is an α-space [36, 39], one derives the formula expressing the minimum number of d-convex pieces into which a geometric n-dimensional polyhedron with holes can be partitioned. The problem of partitioning a geometric n-dimensional polyhedron has many theoretical and practical applications in various fields such as computational geometry, image processing, pattern recognition, computer graphics, VLSI engineering, and others [5, 10, 11, 19, 21, 28, 29, 31, 43]. Mathematics Subject Classification: 68U05, 52A30, 57Q05

Keywords

• geometric n-dimensional polyhedron
• d-convexity
• CW complex
• dividing