Geometric Object Enumeration

Years and Authors of Summarized Original Work

• 2001; Li, Nakano

• 2001; Nakano

• 2004; Nakano

Problem Definition

Enumerating objects with the given property is one of basic problems in mathematics. We review some geometric objects enumeration problems and algorithms to solve them.

A graph is planar if it can be embedded in the plane so that no two edges intersect geometrically except at a vertex to which they are both incident. A plane graph is a planar graph with a fixed planar embedding. A plane graph divides the plane into connected regions called faces. The unbounded face is called the outer face, and other faces are called inner faces.

A plane graph is a floor plan if each face (including the outer face) is a rectangle. A based floor plan is a floor plan with one designated line on the contour of the outer face. The designated line is called the baseline and we always draw the base line as the lowermost horizontal line of the drawing. The 25 based floor plans having 4 inner faces are...