The Embroidery Problem

We consider the problem of embroidering a design pattern, given by a graph G, using a single minimum length thread. We give an exact polynomial-time algorithm for the case that G is connected. If G has multiple connected components, then we show that the problem is NP-hard and give a polynomial-time 2-approximation algorithm. We also present results for special cases of the problem with various objective functions.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Esther M. Arkin, George Hart, Joondong Kim, Irina Kostitsyna, Joseph S. B. Mitchell, Girishkumar Sabhnani, Steven Skiena
• Keywords: CCCG 2008, Computational Geometry, Exact Polynomial-time Algorithm, Polynomial-time 2-approximation Algorithm, Single Minimum Length