On the complexity of constructing Golomb Rulers

A Golomb Ruler is a ruler with integer marks where the distances between every two marks are distinct. Golomb Rulers find diverse applications in computer science and electrical engineering. According to our knowledge the computational complexity of problems related to the construction of Golomb Rulers is unknown. We provide natural definitions for problems related to the construction of such rulers. The main contribution of this work is NP-completeness results for two such decision problems.