Minimum Forcing Sets for Single-vertex Crease Pattern

Abstract

We propose an algorithm for finding a minimum forcing set of a given flat-foldable single-vertex crease pattern (SVCP). SVCP consists of straight lines called creases that can be labeled as mountains or valleys, and the creases are incident to the center of a disk of paper. A forcing set is a subset of given creases that forces all other creases to fold according to the given labels. Our algorithm is a modification of an existing algorithm for 1D origami. We show that the size of a minimum forcing set of an SVCP is n/2 or n/2+1 where n is the number of creases in the SVCP.